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Tree snumeration polynomials on separable permutations 可分离排列上的树和多项式
Enumerative Combinatorics and Applications Pub Date : 2023-06-17 DOI: 10.54550/eca2024v4s1r6
Yibo Yibo Gao, Siyu Liu
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引用次数: 0
The sum of width-one tensors 宽度为1张量的和
Enumerative Combinatorics and Applications Pub Date : 2023-06-17 DOI: 10.54550/eca2024v4s1r7
William Q. Erickson, Jan Kretschmann
{"title":"The sum of width-one tensors","authors":"William Q. Erickson, Jan Kretschmann","doi":"10.54550/eca2024v4s1r7","DOIUrl":"https://doi.org/10.54550/eca2024v4s1r7","url":null,"abstract":": This paper generalizes a recent result concerning the sum of width-one matrices; in the present work, we consider width-one tensors of arbitrary dimensions. A tensor is said to be width-one if, when visualized as an array, its nonzero entries lie along a path consisting of steps in the positive directions of the standard coordinate vectors. We prove two formulas to compute the sum of all width-one tensors with fixed dimensions and fixed sum of (nonnegative integer) components. The first formula is obtained by converting width-one tensors into tuples of one-row semistandard Young tableaux (thereby inverting the northwest corner rule from optimal transport theory). The second formula, which extracts coefficients from products of multiset Eulerian polynomials, is derived via Stanley–Reisner theory, making use of the EL-shelling of the order complex on the standard basis of tensors.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"275 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122810803","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}
引用次数: 0
Interview with Francesco Brenti 采访弗朗西斯科·布伦蒂
Enumerative Combinatorics and Applications Pub Date : 2023-06-16 DOI: 10.54550/eca2024v4s1i1
T. Mansour, Annamaria Brenti
{"title":"Interview with Francesco Brenti","authors":"T. Mansour, Annamaria Brenti","doi":"10.54550/eca2024v4s1i1","DOIUrl":"https://doi.org/10.54550/eca2024v4s1i1","url":null,"abstract":"Photo by Annamaria Brenti Francesco Brenti completed his Ph.D. at the Massachusetts Institute of Technology (MIT) in 1988 under the supervision of Richard Stanley. During his career, he worked at MIT (1984-1988), the University of Michigan (1988-1991), the Mittag-Leffler Institute (1991-1992), the University of Perugia (1992-1997), and the University of Rome “Tor Vergata” (1997-present). Since 2013, he has been a full professor at the University of Rome “Tor Vergata.” His visiting positions include the Hebrew University of Jerusalem; the University of Marne-la-Vallée, Noisy-le-Grand; the Institute for Advanced Study, Princeton; the Mathematical Sciences Research Institute, Berkeley; the Royal Institute of Technology, Stockholm; the Mathematical Research Centre, Aarhus; Bar-Ilan University, Ramat Gan; MIT; the Mittag-Leffler Institute, Djursholm. His research interests are in algebraic combinatorics, KazhdanLusztig theory, the theory of symmetric functions, and total positivity. He is a member of the editorial boards of the Séminaire Lotharingien de Combinatoire (since 1997), the European Journal of Combinatorics (since 2008), Algebraic Combinatorics (since 2020), and Bollettino dell’Unione Matematica Italiana (since 2020).","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122711024","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}
引用次数: 0
q-Enumeration of type B and type D Eulerian polynomials based on parity of descents 基于降宇称的B型和D型欧拉多项式的枚举
Enumerative Combinatorics and Applications Pub Date : 2023-06-16 DOI: 10.54550/eca2024v4s1r3
Hiranya Kishore Dey, U. Shankar, S. Sivasubramanian
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引用次数: 1
On the number of bracelets whose co-periods divide a given integer 同周期除以给定整数的手镯的个数
Enumerative Combinatorics and Applications Pub Date : 2023-03-31 DOI: 10.54550/eca2023v3s3r23
P. Hadjicostas
{"title":"On the number of bracelets whose co-periods divide a given integer","authors":"P. Hadjicostas","doi":"10.54550/eca2023v3s3r23","DOIUrl":"https://doi.org/10.54550/eca2023v3s3r23","url":null,"abstract":",","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132815578","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}
引用次数: 0
Interview with Douglas West 道格拉斯·韦斯特访谈
Enumerative Combinatorics and Applications Pub Date : 2023-03-31 DOI: 10.54550/eca2023v3s3i8
T. Mansour
{"title":"Interview with Douglas West","authors":"T. Mansour","doi":"10.54550/eca2023v3s3i8","DOIUrl":"https://doi.org/10.54550/eca2023v3s3i8","url":null,"abstract":"Photo by University of Illinois Urbana-Champaign, College of Liberal Arts & Sciences Douglas B. West completed his undergraduate studies at Princeton University in 1974. He obtained his Ph.D. in 1978 at the Massachusetts Institute of Technology under the supervision of Daniel J. Kleitman. During his career, he taught and conducted research at Stanford University (1978–79), Princeton University (1979–82), the University of California, Berkeley (1989–90), the University of Illinois (1982–present), and Zhejiang Normal University (2012–present). Since 2011 he has been a Professor Emeritus at the University of Illinois. Professor West has been the Editor-in-Chief of the journal Discrete Mathematics since 2017 and has advised 38 Ph.D. theses. He has hosted an up-to-date listing of conferences in discrete mathematics on his homepage since 1997 and is known for his textbooks Introduction to Graph Theory (Prentice-Hall 1996, 2001) and Combinatorial Mathematics (Cambridge 2021).","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122468868","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}
引用次数: 0
Some linear transformations on symmetric functions arising from a Formula of Thiel and Williams 由Thiel和Williams公式导出的对称函数上的一些线性变换
Enumerative Combinatorics and Applications Pub Date : 2023-03-31 DOI: 10.54550/eca2023v3s3r24
Teresa Li, Lili Mu, Richard Stanley
{"title":"Some linear transformations on symmetric functions arising from a Formula of Thiel and Williams","authors":"Teresa Li, Lili Mu, Richard Stanley","doi":"10.54550/eca2023v3s3r24","DOIUrl":"https://doi.org/10.54550/eca2023v3s3r24","url":null,"abstract":"","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"309 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135949919","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}
引用次数: 0
Interview with Joel Spencer 乔尔·斯宾塞访谈
Enumerative Combinatorics and Applications Pub Date : 2023-03-31 DOI: 10.54550/eca2023v3s3i7
J. Spencer, T. Mansour
{"title":"Interview with Joel Spencer","authors":"J. Spencer, T. Mansour","doi":"10.54550/eca2023v3s3i7","DOIUrl":"https://doi.org/10.54550/eca2023v3s3i7","url":null,"abstract":"Photo by Mary Ann Spencer. Backdrop is Aurora in St. Petersburg. Joel Spencer completed his Ph.D. at Harvard University in 1970 under the supervision of Andrew Gleason. During his career he worked at UCLA (1971-1972), MIT (1972-1975), and Stony Brook University (1975-1988). Since 1988 he has been a professor at NYU’s Courant Institute of Mathematical Sciences. He has held visiting positions in Budapest (as a N.A.S. Exchange Fellow), the Weizmann Institute, Reading, MIT, the Institute for Mathematics and Its Applications, the Institute for Advanced Study, Melbourne, and at the Mittag-Leffler Institute. He is a Co-Founder and Co-Editor-in-Chief of journal Random Structures and Algorithms (1990-2007) and also a member of the Editorial Board for the journals Combinatorica (1979-2009); American Math Monthly (1986-1991); Discrete Mathematics (1988-1996); The Annals of Applied Probability (1990-1994). He was an invited speaker at the International Congress of Mathematics in Zürich in 1994. In 2012 he was made a Fellow of the AMS and in 2017 became a SIAM Fellow. In 2021 he received the Leroy P. Steele Prize for mathematical exposition with his coauthor Noga Alon for their book The Probabilistic Method. His Erdős number is one.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131704510","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}
引用次数: 0
On a lemma of Schensted 关于Schensted的引理
Enumerative Combinatorics and Applications Pub Date : 2023-03-28 DOI: 10.54550/eca2023v3s3r19
Antoine Abram, C. Reutenauer
{"title":"On a lemma of Schensted","authors":"Antoine Abram, C. Reutenauer","doi":"10.54550/eca2023v3s3r19","DOIUrl":"https://doi.org/10.54550/eca2023v3s3r19","url":null,"abstract":"We give a direct proof of Schensted's lemma asserting that row and column insertion in a tableau commute.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126878557","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}
引用次数: 0
A cyclic sieving phenomenon for symplectic tableaux 辛表的循环筛分现象
Enumerative Combinatorics and Applications Pub Date : 2023-03-16 DOI: 10.54550/eca2024v4s1r8
Graeme Henrickson, Anna Stokke, Max Wiebe
{"title":"A cyclic sieving phenomenon for symplectic tableaux","authors":"Graeme Henrickson, Anna Stokke, Max Wiebe","doi":"10.54550/eca2024v4s1r8","DOIUrl":"https://doi.org/10.54550/eca2024v4s1r8","url":null,"abstract":"We give a cyclic sieving phenomenon for symplectic $lambda$-tableaux, $SP(lambda, 2m)$, where $lambda$ is a partition of an odd positive integer $n$ and $gcd(m,p)=1$ for any odd prime $pleq n$. We use the crystal structure on Kashiwara-Nakashima symplectic tableaux to get a cyclic sieving action as the product of simple reflections in the Weyl group. The cyclic sieving polynomial is the $q$-anologue of the hook-content formula for symplectic tableaux.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128585312","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}
引用次数: 1
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