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":"66 1","pages":""},"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":"31 1","pages":""},"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":"44 1","pages":""},"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":"17 1","pages":""},"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":"212 1","pages":""},"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":"41 1","pages":""},"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":"51 1","pages":""},"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":"8 1","pages":""},"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":"43 1","pages":""},"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}
Pub Date : 2024-04-08DOI: 10.1080/10586458.2024.2334381
Dazhao Tang
Let pod−k(n) denote the number of partition k-tuples of n where the odd parts in each partition are distinct. By utilizing some q-series manipulations and iterative computations, we derive dozens ...
让 pod-k(n)表示 n 的分区 k 元组数，其中每个分区的奇数部分都是不同的。通过利用一些 q 序列操作和迭代计算，我们得出了几十个 ...
{"title":"Internal Congruences Modulo Powers of 5 for Partition k-Tuples with Odd Parts Distinct","authors":"Dazhao Tang","doi":"10.1080/10586458.2024.2334381","DOIUrl":"https://doi.org/10.1080/10586458.2024.2334381","url":null,"abstract":"Let pod−k(n) denote the number of partition k-tuples of n where the odd parts in each partition are distinct. By utilizing some q-series manipulations and iterative computations, we derive dozens ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140587613","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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