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Mixing on Generalized Associahedra 广义结合面上的混合
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-03-18 DOI: 10.1007/s00026-025-00750-5
William Chang, Colin Defant, Daniel Frishberg
{"title":"Mixing on Generalized Associahedra","authors":"William Chang,&nbsp;Colin Defant,&nbsp;Daniel Frishberg","doi":"10.1007/s00026-025-00750-5","DOIUrl":"10.1007/s00026-025-00750-5","url":null,"abstract":"<div><p>Eppstein and Frishberg recently proved that the mixing time for the simple random walk on the 1-skeleton of the associahedron is <span>(O(n^3log ^3 n))</span>. We obtain similar rapid mixing results for the simple random walks on the 1-skeleta of the type-<i>B</i> and type-<i>D</i> associahedra. We adapt Eppstein and Frishberg’s technique to obtain the same bound of <span>(O(n^3log ^3 n))</span> in type <i>B</i> and a bound of <span>(O(n^{13} log ^2 n))</span> in type <i>D</i>; in the process, we establish an expansion bound that is tight up to logarithmic factors in type <i>B</i>.\u0000</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"921 - 943"},"PeriodicalIF":0.7,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037443","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}
引用次数: 0
Correction to: Positivity Among P-Partition Generating Functions 对p -分区生成函数间正性的修正
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-03-14 DOI: 10.1007/s00026-025-00744-3
Nathan R. T. Lesnevich, Peter R. W. McNamara
{"title":"Correction to: Positivity Among P-Partition Generating Functions","authors":"Nathan R. T. Lesnevich,&nbsp;Peter R. W. McNamara","doi":"10.1007/s00026-025-00744-3","DOIUrl":"10.1007/s00026-025-00744-3","url":null,"abstract":"<div><p>We correct a theorem on caterpillar posets in Lesnevich and McNamara (Ann Comb 26(1):171–204, 2022). In strengthening the hypotheses on the caterpillar posets we consider, we are also able to strengthen the conclusion on the types of positivity that result.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"947 - 953"},"PeriodicalIF":0.7,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00744-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037375","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Crystal Chute Moves on Pipe Dreams 水晶滑道移动管道梦想
IF 0.8 4区 数学
Annals of Combinatorics Pub Date : 2025-03-12 DOI: 10.1007/s00026-025-00747-0
Sarah Gold, Elizabeth Milićević, Yuxuan Sun
{"title":"Crystal Chute Moves on Pipe Dreams","authors":"Sarah Gold,&nbsp;Elizabeth Milićević,&nbsp;Yuxuan Sun","doi":"10.1007/s00026-025-00747-0","DOIUrl":"10.1007/s00026-025-00747-0","url":null,"abstract":"<div><p>Schubert polynomials represent a basis for the cohomology of the complete flag variety and thus play a central role in geometry and combinatorics. In this context, Schubert polynomials are generating functions over various combinatorial objects, such as rc-graphs or reduced pipe dreams. By restricting Bergeron and Billey’s chute moves on rc-graphs, we define a Demazure crystal structure on the monomials of a Schubert polynomial. As a consequence, we provide a method for decomposing Schubert polynomials as sums of key polynomials, complementing related work of Assaf and Schilling via reduced factorizations with cutoff, as well as Lenart’s coplactic operators on biwords.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 2","pages":"305 - 344"},"PeriodicalIF":0.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00026-025-00747-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323005","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimum Quantum Degrees with Maya Diagrams 最小量子度与玛雅图表
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-03-06 DOI: 10.1007/s00026-025-00749-y
Ryan M. Shifler
{"title":"Minimum Quantum Degrees with Maya Diagrams","authors":"Ryan M. Shifler","doi":"10.1007/s00026-025-00749-y","DOIUrl":"10.1007/s00026-025-00749-y","url":null,"abstract":"<div><p>We use Maya diagrams to refine the criterion by Fulton and Woodward for the smallest powers of the quantum parameter <i>q</i> that occur in a product of Schubert classes in the (small) quantum cohomology of partial flags. Our approach using Maya diagrams yields a combinatorial proof that the minimal quantum degrees are unique for partial flags. Furthermore, visual combinatorial rules are given to perform precise calculations.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 2","pages":"395 - 413"},"PeriodicalIF":0.7,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162467","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}
引用次数: 0
A Combinatorial Interpretation of the Series for Rogers–Ramanujan–Gordon Identities when (k=3) Rogers-Ramanujan-Gordon恒等式级数的组合解释 (k=3)
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-02-26 DOI: 10.1007/s00026-025-00745-2
Yalçın Can Kılıç
{"title":"A Combinatorial Interpretation of the Series for Rogers–Ramanujan–Gordon Identities when (k=3)","authors":"Yalçın Can Kılıç","doi":"10.1007/s00026-025-00745-2","DOIUrl":"10.1007/s00026-025-00745-2","url":null,"abstract":"<div><p>In this paper, we give a new combinatorial interpretation for the Rogers–Ramanujan–Gordon partitions for <span>(k=3)</span>. Our interpretation is given by base partition and moves ideas. We conclude the paper with some research questions related to the generalization of this approach.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"979 - 994"},"PeriodicalIF":0.7,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435733","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}
引用次数: 0
Arithmetic Relations Modulo 3, 27 and 81 for Overpartitions 过分区的模3、模27和模81的算术关系
IF 0.8 4区 数学
Annals of Combinatorics Pub Date : 2025-02-14 DOI: 10.1007/s00026-025-00746-1
Liang Jin, Li Zhang
{"title":"Arithmetic Relations Modulo 3, 27 and 81 for Overpartitions","authors":"Liang Jin,&nbsp;Li Zhang","doi":"10.1007/s00026-025-00746-1","DOIUrl":"10.1007/s00026-025-00746-1","url":null,"abstract":"<div><p>Let <span>(overline{p}(n))</span> denote the number of overpartitions of <i>n</i>. In this paper, we establish the generating function for <span>(overline{p}(96n+12))</span> modulo 81 using elementary dissection techniques and theta function identities. Based on this generating function and some identities of Ramanujan theta functions <span>(psi (q))</span> and <span>(varphi (-q))</span>, we obtain a congruence relation and an infinite family of congruences modulo 81 for <span>(overline{p}(n))</span>. Furthermore, by studying the periodicity of <span>(psi (q))</span> based on the <span>(ell )</span>-dissection formula of <span>(psi (q))</span> given by Cui and Gu, we find some arithmetic relations and infinite families of congruences modulo 3 and 27 for <span>(overline{p}(n))</span>.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 2","pages":"345 - 363"},"PeriodicalIF":0.8,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323008","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}
引用次数: 0
Bubble Lattices II: Combinatorics 泡格II：组合学
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-02-07 DOI: 10.1007/s00026-025-00743-4
Thomas McConville, Henri Mühle
{"title":"Bubble Lattices II: Combinatorics","authors":"Thomas McConville,&nbsp;Henri Mühle","doi":"10.1007/s00026-025-00743-4","DOIUrl":"10.1007/s00026-025-00743-4","url":null,"abstract":"<div><p>We introduce two simplicial complexes, the noncrossing matching complex and the noncrossing bipartite complex. Both complexes are intimately related to the bubble lattice introduced in our earlier article “Bubble Lattices I: Structure” (arXiv:2202.02874). We study these complexes from both an enumerative and a topological point of view. In particular, we prove that these complexes are shellable and give explicit formulas for certain refined face numbers. Lastly, we conjecture an intriguing connection of these refined face numbers to the so-called <i>M</i>-triangle of the shuffle lattice.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"657 - 690"},"PeriodicalIF":0.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037047","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}
引用次数: 0
The Distribution of the Length of the Longest Path in Random Acyclic Orientations of a Complete Bipartite Graph 完全二部图随机无环方向上最长路径长度的分布
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-01-31 DOI: 10.1007/s00026-025-00741-6
Jessica Khera, Erik Lundberg
{"title":"The Distribution of the Length of the Longest Path in Random Acyclic Orientations of a Complete Bipartite Graph","authors":"Jessica Khera,&nbsp;Erik Lundberg","doi":"10.1007/s00026-025-00741-6","DOIUrl":"10.1007/s00026-025-00741-6","url":null,"abstract":"<div><p>Randomly sampling an acyclic orientation on the complete bipartite graph <span>(K_{n,k})</span> with parts of size <i>n</i> and <i>k</i>, we investigate the length of the longest path. We provide a probability generating function for the distribution of the longest path length, and we use analytic combinatorics to perform asymptotic analysis of the probability distribution in the case of equal part sizes <span>(n=k)</span> tending toward infinity. We show that the distribution is asymptotically Gaussian, and we obtain precise asymptotics for the mean and variance. These results address a question asked by Peter J. Cameron.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 4","pages":"1177 - 1209"},"PeriodicalIF":0.7,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145435865","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}
引用次数: 0
Multiple Series Identities of the Rogers–Ramanujan Type for Overpartition Pairs 过划分对的Rogers-Ramanujan型多重级数恒等式
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2025-01-27 DOI: 10.1007/s00026-025-00742-5
Nancy S. S. Gu, Dan-Tong Wang
{"title":"Multiple Series Identities of the Rogers–Ramanujan Type for Overpartition Pairs","authors":"Nancy S. S. Gu,&nbsp;Dan-Tong Wang","doi":"10.1007/s00026-025-00742-5","DOIUrl":"10.1007/s00026-025-00742-5","url":null,"abstract":"<div><p>The Rogers–Ramanujan identities, which were first introduced by Rogers and then rediscovered by Ramanujan, have attracted a lot of attention. In 1961, Gordon considered the combinatorial generalization of these two identities. Then, in view of the <i>q</i>-difference equations for certain basic hypergeometric series, Andrews derived an analytic version of Gordon’s theorem involving multiple series. Later, Bressoud established a companion for even moduli. Then, subsequent research has been focused on overpartition analogues. In this paper, with the aid of some <i>q</i>-difference equations, we establish the overpartition pair analogues of the aforementioned two theorems due to Gordon and Bressoud. Meanwhile, the corresponding multiple series identities of the Rogers–Ramanujan type are derived by the Bailey pair method. Furthermore, we use the Gordon markings of overpartition pairs to give the combinatorial interpretations of the multiple series.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"30 1","pages":"91 - 130"},"PeriodicalIF":0.7,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561756","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}
引用次数: 0
The Connectivity of Friends-and-Strangers Graphs on Complete Multipartite Graphs 完全多部图上朋友与陌生人图的连通性
IF 0.7 4区 数学
Annals of Combinatorics Pub Date : 2024-12-31 DOI: 10.1007/s00026-024-00740-z
Honglin Zhu
{"title":"The Connectivity of Friends-and-Strangers Graphs on Complete Multipartite Graphs","authors":"Honglin Zhu","doi":"10.1007/s00026-024-00740-z","DOIUrl":"10.1007/s00026-024-00740-z","url":null,"abstract":"<div><p>For simple graphs <i>X</i> and <i>Y</i> on <i>n</i> vertices, the friends-and-strangers graph <span>(textsf{FS}(X,Y))</span> is the graph whose vertex set consists of all bijections <span>(sigma : V(X) rightarrow V(Y))</span>, where two bijections <span>(sigma )</span> and <span>(sigma ')</span> are adjacent if and only if they agree on all but two adjacent vertices <span>(a, b in V(X))</span> such that <span>(sigma (a), sigma (b) in V(Y))</span> are adjacent in <i>Y</i>. Resolving a conjecture of Wang, Lu, and Chen, we completely characterize the connectedness of <span>(textsf{FS}(X, Y))</span> when <i>Y</i> is a complete bipartite graph. We further extend this result to when <i>Y</i> is a complete multipartite graph. We also determine when <span>(textsf{FS}(X, Y))</span> has exactly two connected components where <i>X</i> is bipartite and <i>Y</i> is a complete bipartite graph.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"29 3","pages":"691 - 718"},"PeriodicalIF":0.7,"publicationDate":"2024-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145037552","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}
引用次数: 0
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