For positive integers $n,k$ and $t$, the uniform subset graph $G(n, k, t)$ has all $k$-subsets of ${1,2,ldots, n}$ as vertices and two $k$-subsets are joined by an edge if they intersect at exactly $t$ elements. The Johnson graph $J(n,k)$ corresponds to $G(n,k,k-1)$, that is, two vertices of $J(n,k)$ are adjacent if the intersection of the corresponding $k$-subsets has size $k-1$. A super vertex-cut of a connected graph is a set of vertices whose removal disconnects the graph without isolating a vertex and the super-connectivity is the size of a minimum super vertex-cut. In this work, we fully determine the super-connectivity of the family of Johnson graphs $J(n,k)$ for $ngeq kgeq 1$.
{"title":"The super-connectivity of Johnson graphs","authors":"Gülnaz Boruzanli Ekinci, John Baptist Gauci","doi":"10.23638/DMTCS-22-1-12","DOIUrl":"https://doi.org/10.23638/DMTCS-22-1-12","url":null,"abstract":"For positive integers $n,k$ and $t$, the uniform subset graph $G(n, k, t)$ has all $k$-subsets of ${1,2,ldots, n}$ as vertices and two $k$-subsets are joined by an edge if they intersect at exactly $t$ elements. The Johnson graph $J(n,k)$ corresponds to $G(n,k,k-1)$, that is, two vertices of $J(n,k)$ are adjacent if the intersection of the corresponding $k$-subsets has size $k-1$. A super vertex-cut of a connected graph is a set of vertices whose removal disconnects the graph without isolating a vertex and the super-connectivity is the size of a minimum super vertex-cut. In this work, we fully determine the super-connectivity of the family of Johnson graphs $J(n,k)$ for $ngeq kgeq 1$.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129296039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The majorization relation orders the degree sequences of simple graphs into posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris (2002), the degree sequences of threshold and split graphs form upward-closed sets within the dominance orders they belong to, i.e., any degree sequence majorizing a split or threshold sequence must itself be split or threshold, respectively. Motivated by the fact that threshold graphs and split graphs have characterizations in terms of forbidden induced subgraphs, we define a class $mathcal{F}$ of graphs to be dominance monotone if whenever no realization of $e$ contains an element $mathcal{F}$ as an induced subgraph, and $d$ majorizes $e$, then no realization of $d$ induces an element of $mathcal{F}$. We present conditions necessary for a set of graphs to be dominance monotone, and we identify the dominance monotone sets of order at most 3.
{"title":"Upward-closed hereditary families in the dominance order","authors":"Michael D. Barrus, Jean Guillaume","doi":"10.46298/dmtcs.5666","DOIUrl":"https://doi.org/10.46298/dmtcs.5666","url":null,"abstract":"The majorization relation orders the degree sequences of simple graphs into\u0000posets called dominance orders. As shown by Ruch and Gutman (1979) and Merris\u0000(2002), the degree sequences of threshold and split graphs form upward-closed\u0000sets within the dominance orders they belong to, i.e., any degree sequence\u0000majorizing a split or threshold sequence must itself be split or threshold,\u0000respectively. Motivated by the fact that threshold graphs and split graphs have\u0000characterizations in terms of forbidden induced subgraphs, we define a class\u0000$mathcal{F}$ of graphs to be dominance monotone if whenever no realization of\u0000$e$ contains an element $mathcal{F}$ as an induced subgraph, and $d$ majorizes\u0000$e$, then no realization of $d$ induces an element of $mathcal{F}$. We present\u0000conditions necessary for a set of graphs to be dominance monotone, and we\u0000identify the dominance monotone sets of order at most 3.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"13 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133919275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Given a boolean predicate $Pi$ on labeled networks (e.g., proper coloring, leader election, etc.), a self-stabilizing algorithm for $Pi$ is a distributed algorithm that can start from any initial configuration of the network (i.e., every node has an arbitrary value assigned to each of its variables), and eventually converge to a configuration satisfying $Pi$. It is known that leader election does not have a deterministic self-stabilizing algorithm using a constant-size register at each node, i.e., for some networks, some of their nodes must have registers whose sizes grow with the size $n$ of the networks. On the other hand, it is also known that leader election can be solved by a deterministic self-stabilizing algorithm using registers of $O(log log n)$ bits per node in any $n$-node bounded-degree network. We show that this latter space complexity is optimal. Specifically, we prove that every deterministic self-stabilizing algorithm solving leader election must use $Omega(log log n)$-bit per node registers in some $n$-node networks. In addition, we show that our lower bounds go beyond leader election, and apply to all problems that cannot be solved by anonymous algorithms.
{"title":"Optimal Space Lower Bound for Deterministic Self-Stabilizing Leader Election Algorithms","authors":"Lélia Blin, Laurent Feuilloley, Gabriel Le Bouder","doi":"10.46298/dmtcs.9335","DOIUrl":"https://doi.org/10.46298/dmtcs.9335","url":null,"abstract":"Given a boolean predicate $Pi$ on labeled networks (e.g., proper coloring,\u0000leader election, etc.), a self-stabilizing algorithm for $Pi$ is a distributed\u0000algorithm that can start from any initial configuration of the network (i.e.,\u0000every node has an arbitrary value assigned to each of its variables), and\u0000eventually converge to a configuration satisfying $Pi$. It is known that\u0000leader election does not have a deterministic self-stabilizing algorithm using\u0000a constant-size register at each node, i.e., for some networks, some of their\u0000nodes must have registers whose sizes grow with the size $n$ of the networks.\u0000On the other hand, it is also known that leader election can be solved by a\u0000deterministic self-stabilizing algorithm using registers of $O(log log n)$\u0000bits per node in any $n$-node bounded-degree network. We show that this latter\u0000space complexity is optimal. Specifically, we prove that every deterministic\u0000self-stabilizing algorithm solving leader election must use $Omega(log log\u0000n)$-bit per node registers in some $n$-node networks. In addition, we show that\u0000our lower bounds go beyond leader election, and apply to all problems that\u0000cannot be solved by anonymous algorithms.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122562327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
É. Czabarka, P. Dankelmann, Trevor Olsen, L. Székely
Let $G$ be a a connected graph. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices. We provide asymptotic formulae for the maximum Wiener index of simple triangulations and quadrangulations with given connectivity, as the order increases, and make conjectures for the extremal triangulations and quadrangulations based on computational evidence. If $overline{sigma}(v)$ denotes the arithmetic mean of the distances from $v$ to all other vertices of $G$, then the remoteness of $G$ is defined as the largest value of $overline{sigma}(v)$ over all vertices $v$ of $G$. We give sharp upper bounds on the remoteness of simple triangulations and quadrangulations of given order and connectivity.
{"title":"Wiener Index and Remoteness in Triangulations and Quadrangulations","authors":"É. Czabarka, P. Dankelmann, Trevor Olsen, L. Székely","doi":"10.46298/dmtcs.6473","DOIUrl":"https://doi.org/10.46298/dmtcs.6473","url":null,"abstract":"Let $G$ be a a connected graph. The Wiener index of a connected graph is the\u0000sum of the distances between all unordered pairs of vertices. We provide\u0000asymptotic formulae for the maximum Wiener index of simple triangulations and\u0000quadrangulations with given connectivity, as the order increases, and make\u0000conjectures for the extremal triangulations and quadrangulations based on\u0000computational evidence. If $overline{sigma}(v)$ denotes the arithmetic mean\u0000of the distances from $v$ to all other vertices of $G$, then the remoteness of\u0000$G$ is defined as the largest value of $overline{sigma}(v)$ over all vertices\u0000$v$ of $G$. We give sharp upper bounds on the remoteness of simple\u0000triangulations and quadrangulations of given order and connectivity.\u0000","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134113542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
After fixing a canonical ordering (or labeling) of the elements of a finite poset, one can associate each linear extension of the poset with a permutation. Some recent papers consider specific families of posets and ask how many linear extensions give rise to permutations that avoid certain patterns. We build off of two of these papers. We first consider pattern avoidance in $k$-ary heaps, where we obtain a general result that proves a conjecture of Levin, Pudwell, Riehl, and Sandberg in a special case. We then prove some conjectures that Anderson, Egge, Riehl, Ryan, Steinke, and Vaughan made about pattern-avoiding linear extensions of rectangular posets.
{"title":"Proofs of Conjectures about Pattern-Avoiding Linear Extensions","authors":"Colin Defant","doi":"10.23638/DMTCS-21-4-16","DOIUrl":"https://doi.org/10.23638/DMTCS-21-4-16","url":null,"abstract":"After fixing a canonical ordering (or labeling) of the elements of a finite poset, one can associate each linear extension of the poset with a permutation. Some recent papers consider specific families of posets and ask how many linear extensions give rise to permutations that avoid certain patterns. We build off of two of these papers. We first consider pattern avoidance in $k$-ary heaps, where we obtain a general result that proves a conjecture of Levin, Pudwell, Riehl, and Sandberg in a special case. We then prove some conjectures that Anderson, Egge, Riehl, Ryan, Steinke, and Vaughan made about pattern-avoiding linear extensions of rectangular posets.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130702697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A graph $G$ is a cocomparability graph if there exists an acyclic transitive orientation of the edges of its complement graph $overline{G}$. LBFS$^{+}$ is a graph variant of the generic LBFS, which uses a specific tie-breaking mechanism. Starting with some ordering $sigma_{0}$ of $G$, let ${sigma_{i}}_{igeq 1}$ be the sequence of orderings such that $sigma_{i}=$LBFS$^{+}(G, sigma_{i-1})$. The LexCycle($G$) is defined as the maximum length of a cycle of vertex orderings of $G$ obtained via such a sequence of LBFS$^{+}$ sweeps. Dusart and Habib [Discrete Appl. Math., 216 (2017), pp. 149-161] conjectured that LexCycle($G$)=2 if $G$ is a cocomparability graph and proved it holds for interval graphs. In this paper, we show that LexCycle($G$)=2 if $G$ is a $overline{P_{2}cup P_{3}}$-free cocomparability graph, where a $overline{P_{2}cup P_{3}}$ is the graph whose complement is the disjoint union of $P_{2}$ and $P_{3}$. As corollaries, it's applicable for diamond-free cocomparability graphs, cocomparability graphs with girth at least 4, as well as interval graphs.
{"title":"The LexCycle on $overline{P_{2}cup P_{3}}$-free Cocomparability Graphs","authors":"Xiaolu Gao, Shoujun Xu","doi":"10.23638/DMTCS-22-4-13","DOIUrl":"https://doi.org/10.23638/DMTCS-22-4-13","url":null,"abstract":"A graph $G$ is a cocomparability graph if there exists an acyclic transitive orientation of the edges of its complement graph $overline{G}$. LBFS$^{+}$ is a graph variant of the generic LBFS, which uses a specific tie-breaking mechanism. Starting with some ordering $sigma_{0}$ of $G$, let ${sigma_{i}}_{igeq 1}$ be the sequence of orderings such that $sigma_{i}=$LBFS$^{+}(G, sigma_{i-1})$. The LexCycle($G$) is defined as the maximum length of a cycle of vertex orderings of $G$ obtained via such a sequence of LBFS$^{+}$ sweeps. Dusart and Habib [Discrete Appl. Math., 216 (2017), pp. 149-161] conjectured that LexCycle($G$)=2 if $G$ is a cocomparability graph and proved it holds for interval graphs. In this paper, we show that LexCycle($G$)=2 if $G$ is a $overline{P_{2}cup P_{3}}$-free cocomparability graph, where a $overline{P_{2}cup P_{3}}$ is the graph whose complement is the disjoint union of $P_{2}$ and $P_{3}$. As corollaries, it's applicable for diamond-free cocomparability graphs, cocomparability graphs with girth at least 4, as well as interval graphs.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134533291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all (finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can actually be found in that sequence as segments (up to exchange of letters in the infinite case). This result was previously attributed to unpublished work by D. Guaiana and may also be derived from publications of A. Shur only available in Russian. We also identify the (finitely many) finite binary patterns that appear non trivially, in the sense that they are obtained by applying an endomorphism that does not map the set of all segments of the sequence into itself.
{"title":"Binary patterns in the Prouhet-Thue-Morse sequence","authors":"J. Almeida, Ondvrej Kl'ima","doi":"10.46298/dmtcs.5460","DOIUrl":"https://doi.org/10.46298/dmtcs.5460","url":null,"abstract":"We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all\u0000(finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can\u0000actually be found in that sequence as segments (up to exchange of letters in\u0000the infinite case). This result was previously attributed to unpublished work\u0000by D. Guaiana and may also be derived from publications of A. Shur only\u0000available in Russian. We also identify the (finitely many) finite binary\u0000patterns that appear non trivially, in the sense that they are obtained by\u0000applying an endomorphism that does not map the set of all segments of the\u0000sequence into itself.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"100 5 Pt 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131402105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Under what circumstances might every extension of a combinatorial structure contain more copies of another one than the original did? This property, which we call prolificity, holds universally in some cases (e.g., finite linear orders) and only trivially in others (e.g., permutations). Integer compositions, or equivalently layered permutations, provide a middle ground. In that setting, there are prolific compositions for a given pattern if and only if that pattern begins and ends with 1. For each pattern, there is an easily constructed automaton that recognises prolific compositions for that pattern. Some instances where there is a unique minimal prolific composition for a pattern are classified.
{"title":"Prolific Compositions","authors":"Murray Tannock, M. Albert","doi":"10.23638/DMTCS-21-2-10","DOIUrl":"https://doi.org/10.23638/DMTCS-21-2-10","url":null,"abstract":"Under what circumstances might every extension of a combinatorial structure contain more copies of another one than the original did? This property, which we call prolificity, holds universally in some cases (e.g., finite linear orders) and only trivially in others (e.g., permutations). Integer compositions, or equivalently layered permutations, provide a middle ground. In that setting, there are prolific compositions for a given pattern if and only if that pattern begins and ends with 1. For each pattern, there is an easily constructed automaton that recognises prolific compositions for that pattern. Some instances where there is a unique minimal prolific composition for a pattern are classified.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"513 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116379437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We give three applications of a recently-proven ``Decomposition Lemma," which allows one to count preimages of certain sets of permutations under West's stack-sorting map $s$. We first enumerate the permutation class $s^{-1}(text{Av}(231,321))=text{Av}(2341,3241,45231)$, finding a new example of an unbalanced Wilf equivalence. This result is equivalent to the enumeration of permutations sortable by ${bf B}circ s$, where ${bf B}$ is the bubble sort map. We then prove that the sets $s^{-1}(text{Av}(231,312))$, $s^{-1}(text{Av}(132,231))=text{Av}(2341,1342,underline{32}41,underline{31}42)$, and $s^{-1}(text{Av}(132,312))=text{Av}(1342,3142,3412,34underline{21})$ are counted by the so-called ``Boolean-Catalan numbers," settling a conjecture of the current author and another conjecture of Hossain. This completes the enumerations of all sets of the form $s^{-1}(text{Av}(tau^{(1)},ldots,tau^{(r)}))$ for ${tau^{(1)},ldots,tau^{(r)}}subseteq S_3$ with the exception of the set ${321}$. We also find an explicit formula for $|s^{-1}(text{Av}_{n,k}(231,312,321))|$, where $text{Av}_{n,k}(231,312,321)$ is the set of permutations in $text{Av}_n(231,312,321)$ with $k$ descents. This allows us to prove a conjectured identity involving Catalan numbers and order ideals in Young's lattice.
{"title":"Enumeration of Stack-Sorting Preimages via a Decomposition Lemma","authors":"Colin Defant","doi":"10.46298/dmtcs.6709","DOIUrl":"https://doi.org/10.46298/dmtcs.6709","url":null,"abstract":"We give three applications of a recently-proven ``Decomposition Lemma,\" which allows one to count preimages of certain sets of permutations under West's stack-sorting map $s$. We first enumerate the permutation class $s^{-1}(text{Av}(231,321))=text{Av}(2341,3241,45231)$, finding a new example of an unbalanced Wilf equivalence. This result is equivalent to the enumeration of permutations sortable by ${bf B}circ s$, where ${bf B}$ is the bubble sort map. We then prove that the sets $s^{-1}(text{Av}(231,312))$, $s^{-1}(text{Av}(132,231))=text{Av}(2341,1342,underline{32}41,underline{31}42)$, and $s^{-1}(text{Av}(132,312))=text{Av}(1342,3142,3412,34underline{21})$ are counted by the so-called ``Boolean-Catalan numbers,\" settling a conjecture of the current author and another conjecture of Hossain. This completes the enumerations of all sets of the form $s^{-1}(text{Av}(tau^{(1)},ldots,tau^{(r)}))$ for ${tau^{(1)},ldots,tau^{(r)}}subseteq S_3$ with the exception of the set ${321}$. We also find an explicit formula for $|s^{-1}(text{Av}_{n,k}(231,312,321))|$, where $text{Av}_{n,k}(231,312,321)$ is the set of permutations in $text{Av}_n(231,312,321)$ with $k$ descents. This allows us to prove a conjectured identity involving Catalan numbers and order ideals in Young's lattice.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127252903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article we consider square permutations, a natural subclass of permutations defined in terms of geometric conditions, that can also be described in terms of pattern avoiding permutations, and convex permutoninoes, a related subclass of polyominoes. While these two classes of objects arised independently in various contexts, they play a natural role in the description of certain random horizontally and vertically convex grid configurations. We propose a common approach to the enumeration of these two classes of objets that allows us to explain the known common form of their generating functions, and to derive new refined formulas and linear time random generation algorithms for these objects and the associated grid configurations.
{"title":"A code for square permutations and convex permutominoes","authors":"E. Duchi","doi":"10.23638/DMTCS-21-2-2","DOIUrl":"https://doi.org/10.23638/DMTCS-21-2-2","url":null,"abstract":"In this article we consider square permutations, a natural subclass of permutations defined in terms of geometric conditions, that can also be described in terms of pattern avoiding permutations, and convex permutoninoes, a related subclass of polyominoes. While these two classes of objects arised independently in various contexts, they play a natural role in the description of certain random horizontally and vertically convex grid configurations. \u0000We propose a common approach to the enumeration of these two classes of objets that allows us to explain the known common form of their generating functions, and to derive new refined formulas and linear time random generation algorithms for these objects and the associated grid configurations.","PeriodicalId":110830,"journal":{"name":"Discret. Math. Theor. Comput. Sci.","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127361064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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