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Journal of Combinatorics最新文献

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Graph Theory: Part 2 图论:第2部分
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2019-01-01 DOI: 10.1007/978-3-030-00831-4_9
P. Mladenovic
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引用次数: 1
Mathematical Games 数学游戏
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2019-01-01 DOI: 10.1007/978-3-030-00831-4_11
P. Mladenovic
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引用次数: 0
Generating Functions 生成函数
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2019-01-01 DOI: 10.1007/978-3-030-00831-4_5
P. Mladenovic
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引用次数: 0
Inclusion-Exclusion Principle 容斥原理
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2019-01-01 DOI: 10.1007/978-3-030-00831-4_4
P. Mladenovic
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引用次数: 0
Binomial and Multinomial Theorems 二项式和多项定理
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2019-01-01 DOI: 10.1007/978-3-030-00831-4_3
P. Mladenovic
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引用次数: 0
Pak–Stanley labeling for central graphical arrangements 中央图形排列的Pak-Stanley标记
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2018-11-29 DOI: 10.4310/joc.2021.v12.n4.a1
M. Mazin, Joshua Miller
The original Pak-Stanley labeling was defined by Pak and Stanley as a bijective map from the set of regions of an extended Shi arrangement to the set of parking functions. This map was later generalized to other arrangements associated with graphs and directed multigraphs. In these more general cases the map is no longer bijective. However, it was shown Hopkins and Perkinson and then the first author that it is surjective to the set of the $G$-parking functions, where $G$ is the multigraph associated with the arrangement. This leads to a natural question: when is the generalized Pak-Stanley map bijective? In this paper we answer this question in the special case of centered hyperplane arrangements, i.e. the case when all the hyperplanes of the arrangement pass through a common point.
最初的Pak-Stanley标记被Pak和Stanley定义为从扩展的Shi排列的区域集到停车函数集的双射映射。这个图后来被推广到与图和有向多图有关的其他排列。在这些更一般的情况下,地图不再是双射的。然而,Hopkins和Perkinson以及后来的第一作者证明了它是$G$停放函数集合的满射,其中$G$是与排列相关的多图。这就引出了一个很自然的问题:广义Pak-Stanley映射什么时候是双射的?本文在有心超平面排列的特殊情况下,即所有的超平面都经过一个公点的情况下,回答了这个问题。
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引用次数: 0
Some conjectures on the Schur expansion of Jack polynomials 关于Jack多项式的Schur展开的一些猜想
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2018-10-26 DOI: 10.4310/joc.2021.v12.n2.a2
P. Alexandersson, J. Haglund, George Wang
We present positivity conjectures for the Schur expansion of Jack symmetric functions in two bases given by binomial coefficients. Partial results suggest that there are rich combinatorics to be found in these bases, including Eulerian numbers, Stirling numbers, quasi-Yamanouchi tableaux, and rook boards. These results also lead to further conjectures about the fundamental quasisymmetric expansions of these bases, which we prove for special cases.
给出了二项式系数给出的两基中Jack对称函数的Schur展开式的正猜想。部分结果表明,在这些基中存在丰富的组合,包括欧拉数、斯特林数、拟山内图和车棋盘。这些结果还导致了关于这些基的基本准对称展开的进一步猜想,我们在特殊情况下证明了这些猜想。
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引用次数: 2
Relations in doubly laced crystal graphs via discrete Morse theory 用离散莫尔斯理论研究双条纹晶体图中的关系
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2018-10-10 DOI: 10.4310/joc.2021.v12.n1.a5
Molly Lynch
We study the combinatorics of crystal graphs given by highest weight representations of types $A_{n}, B_{n}, C_{n}$, and $D_{n}$, uncovering new relations that exist among crystal operators. Much structure in these graphs has been revealed by local relations given by Stembridge and Sternberg. However, there exist relations among crystal operators that are not implied by Stembridge or Sternberg relations. Viewing crystal graphs as edge colored posets, we use poset topology to study them. Using the lexicographic discrete Morse functions of Babson and Hersh, we relate the Mobius function of a given interval in a crystal poset of simply laced or doubly laced type to the types of relations that can occur among crystal operators within this interval. For a crystal of a highest weight representation of finite classical Cartan type, we show that whenever there exists an interval whose Mobius function is not equal to -1, 0, or 1, there must be a relation among crystal operators within this interval not implied by Stembridge or Sternberg relations. As an example of an application, this yields relations among crystal operators in type $C_{n}$ that were not previously known. Additionally, by studying the structure of Sternberg relations in the doubly laced case, we prove that crystals of highest weight representations of types $B_{2}$ and $C_{2}$ are not lattices.
我们研究了由类型$A_{n}, B_{n}, C_{n}$和$D_{n}$的最高权表示给出的晶体图的组合,揭示了晶体算子之间存在的新关系。Stembridge和Sternberg给出的局部关系揭示了这些图中的许多结构。然而,晶体算符之间存在着没有被Stembridge关系或Sternberg关系所暗示的关系。将晶体图视为边缘彩色偏序集,利用偏序集拓扑对其进行研究。利用Babson和Hersh的字典学离散莫尔斯函数,我们将单列或双列型晶体偏序集中给定区间的莫比乌斯函数与该区间内晶体算子之间可能发生的关系类型联系起来。对于具有最高权值表示的有限经典Cartan型晶体,我们证明了只要存在一个莫比乌斯函数不等于- 1,0或1的区间,那么在这个区间内的晶体算子之间一定存在一个不被Stembridge或Sternberg关系所暗示的关系。作为一个应用程序的例子,这产生了$C_{n}$类型的晶体操作符之间的关系,这些关系以前是不知道的。此外,通过研究双条纹情况下Sternberg关系的结构,我们证明了$B_{2}$和$C_{2}$类型的最高权重表示的晶体不是晶格。
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引用次数: 0
Fertility numbers 生育数量
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2018-09-11 DOI: 10.4310/joc.2020.v11.n3.a6
Colin Defant
A nonnegative integer is called a fertility number if it is equal to the number of preimages of a permutation under West's stack-sorting map. We prove structural results concerning permutations, allowing us to deduce information about the set of fertility numbers. In particular, the set of fertility numbers is closed under multiplication and contains every nonnegative integer that is not congruent to $3$ modulo $4$. We show that the lower asymptotic density of the set of fertility numbers is at least $1954/2565approx 0.7618$. We also exhibit some positive integers that are not fertility numbers and conjecture that there are infinitely many such numbers.
如果一个非负整数等于一个排列在West的堆栈排序映射下的原象的数目,则称为可育数。我们证明了有关排列的结构结果,使我们能够推断出生育数集的信息。特别地,生育数的集合在乘法下是封闭的,并且包含所有不等于$3$取$4$模的非负整数。我们证明了生育数集合的下渐近密度至少为$1954/2565约0.7618$。我们还展示了一些非生育数的正整数,并推测有无穷多个这样的数。
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引用次数: 18
Designs and Codes 设计及规范
IF 0.3 Q4 MATHEMATICS, APPLIED Pub Date : 2018-09-03 DOI: 10.1142/9789813274334_0004
CodesThann WardSeptember
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引用次数: 1
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Journal of Combinatorics
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