Pub Date : 2024-06-14DOI: 10.1080/10586458.2024.2363508
Maciej Bocheński, Willem A. de Graaf, Piotr Jastrzȩbski, Aleksy Tralle
We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-vir...
{"title":"Non-Virtually Abelian Discontinuous Group Actions vs. Proper SL(2,ℝ) -Actions on Homogeneous Spaces","authors":"Maciej Bocheński, Willem A. de Graaf, Piotr Jastrzȩbski, Aleksy Tralle","doi":"10.1080/10586458.2024.2363508","DOIUrl":"https://doi.org/10.1080/10586458.2024.2363508","url":null,"abstract":"We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-vir...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141518678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-26DOI: 10.1080/10586458.2024.2343846
Joachim Jelisiejew, Kristian Ranestad, Frank-Olaf Schreyer
We discuss the space VPS(Q, H) of ideals with Hilbert function H=(1,n,n,…) that are apolar to a full rank quadric Q. We prove that its components of saturated ideals are closely related to the locu...
{"title":"The Variety of Polar Simplices II","authors":"Joachim Jelisiejew, Kristian Ranestad, Frank-Olaf Schreyer","doi":"10.1080/10586458.2024.2343846","DOIUrl":"https://doi.org/10.1080/10586458.2024.2343846","url":null,"abstract":"We discuss the space VPS(Q, H) of ideals with Hilbert function H=(1,n,n,…) that are apolar to a full rank quadric Q. We prove that its components of saturated ideals are closely related to the locu...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-25DOI: 10.1080/10586458.2024.2336060
Garen Chiloyan
Let E be a Q-isogeny class of elliptic curves defined over Q without CM. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in E and an edge for each Q-isogeny ...
设 E 是定义在 Q 上的无 CM 的椭圆曲线的 Q-isogeny 类。与 E 相关的同源图是这样一个图：E 中的每条椭圆曲线都有一个顶点，每条 Q-isogeny 曲线都有一条边。
{"title":"2-Adic Galois Images of Non-CM Isogeny-Torsion Graphs Defined over ℚ","authors":"Garen Chiloyan","doi":"10.1080/10586458.2024.2336060","DOIUrl":"https://doi.org/10.1080/10586458.2024.2336060","url":null,"abstract":"Let E be a Q-isogeny class of elliptic curves defined over Q without CM. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in E and an edge for each Q-isogeny ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-23DOI: 10.1080/10586458.2024.2340000
Marie-Charlotte Brandenburg, Benjamin Hollering, Irem Portakal
We study the correlated equilibrium polytope PG of a game G from a combinatorial point of view. We introduce the region of full-dimensionality for this class of polytopes and prove that it is a sem...
我们从组合的角度研究博弈 G 的相关均衡多面体 PG。我们引入了这一类多面体的全维区域，并证明它是一个半...
{"title":"Combinatorics of Correlated Equilibria","authors":"Marie-Charlotte Brandenburg, Benjamin Hollering, Irem Portakal","doi":"10.1080/10586458.2024.2340000","DOIUrl":"https://doi.org/10.1080/10586458.2024.2340000","url":null,"abstract":"We study the correlated equilibrium polytope PG of a game G from a combinatorial point of view. We introduce the region of full-dimensionality for this class of polytopes and prove that it is a sem...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140936056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-14DOI: 10.1080/10586458.2024.2340742
Carl P. Dettmann
The three gap theorem states that for any α∈R and N∈N, the number of different gaps between consecutive nα( mod 1) for n∈{1,…,N} is at most 3. Biringer and Schmidt (2008) instead considered the dis...
{"title":"Kronecker Sequences with Many Distances","authors":"Carl P. Dettmann","doi":"10.1080/10586458.2024.2340742","DOIUrl":"https://doi.org/10.1080/10586458.2024.2340742","url":null,"abstract":"The three gap theorem states that for any α∈R and N∈N, the number of different gaps between consecutive nα( mod 1) for n∈{1,…,N} is at most 3. Biringer and Schmidt (2008) instead considered the dis...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-14DOI: 10.1080/10586458.2024.2337223
Giacomo Cherubini, Pavlo Yatsyna
We prove that there exist Salem numbers with trace –3 and every even degree ≥34. Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical...
{"title":"There are Salem Numbers with Trace –3 and Every Degree At Least 34","authors":"Giacomo Cherubini, Pavlo Yatsyna","doi":"10.1080/10586458.2024.2337223","DOIUrl":"https://doi.org/10.1080/10586458.2024.2337223","url":null,"abstract":"We prove that there exist Salem numbers with trace –3 and every even degree ≥34. Our proof combines a theoretical approach, which allows us to treat all sufficiently large degrees, with a numerical...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-13DOI: 10.1080/10586458.2024.2337232
Nicolas Faroß, Moritz Weber
In 2019, Jung–Weber gave an example of a concrete magic unitary M, which defines a C*-algebraic model of the quantum permutation group S4+. We show with the help of a computer that there exist no p...
{"title":"A Concrete Model for the Quantum Permutation Group on 4 Points","authors":"Nicolas Faroß, Moritz Weber","doi":"10.1080/10586458.2024.2337232","DOIUrl":"https://doi.org/10.1080/10586458.2024.2337232","url":null,"abstract":"In 2019, Jung–Weber gave an example of a concrete magic unitary M, which defines a C*-algebraic model of the quantum permutation group S4+. We show with the help of a computer that there exist no p...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-10DOI: 10.1080/10586458.2024.2336074
F. Bergeron
The purpose of this paper is to present conjectures that extend to any “triangular” partitions (partitions “under any line” in the terminology of Blasiak-Haiman-Morse-Pun-Seelinger), properties of ...
{"title":"Triangular Diagonal Harmonics Conjectures","authors":"F. Bergeron","doi":"10.1080/10586458.2024.2336074","DOIUrl":"https://doi.org/10.1080/10586458.2024.2336074","url":null,"abstract":"The purpose of this paper is to present conjectures that extend to any “triangular” partitions (partitions “under any line” in the terminology of Blasiak-Haiman-Morse-Pun-Seelinger), properties of ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-10DOI: 10.1080/10586458.2024.2337229
Wei Wang, Wei Wang
Characterizing graphs by their spectra is a fundamental and challenging problem in spectral graph theory, which has received considerable attention in recent years. A major unsolved conjecture in t...
{"title":"Haemers’ Conjecture: An Algorithmic Perspective","authors":"Wei Wang, Wei Wang","doi":"10.1080/10586458.2024.2337229","DOIUrl":"https://doi.org/10.1080/10586458.2024.2337229","url":null,"abstract":"Characterizing graphs by their spectra is a fundamental and challenging problem in spectral graph theory, which has received considerable attention in recent years. A major unsolved conjecture in t...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-09DOI: 10.1080/10586458.2024.2338279
A. Srinivasan, L. A. Calvo
If the generalized Markoff equation a2+b2+c2=3abc+m has a solution triple, then it has infinitely many solutions. For a positive integer m > 1, we show that all positive solution triples are genera...
如果广义马尔科夫方程 a2+b2+c2=3abc+m 有一个解三元组，那么它就有无穷多个解。对于 m > 1 的正整数，我们证明了所有正解三元组都是属...
{"title":"Counting Minimal Triples for a Generalized Markoff Equation","authors":"A. Srinivasan, L. A. Calvo","doi":"10.1080/10586458.2024.2338279","DOIUrl":"https://doi.org/10.1080/10586458.2024.2338279","url":null,"abstract":"If the generalized Markoff equation a2+b2+c2=3abc+m has a solution triple, then it has infinitely many solutions. For a positive integer m > 1, we show that all positive solution triples are genera...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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