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Enumerative Combinatorics and Applications最新文献

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Counting on matrices 对矩阵进行计数
Enumerative Combinatorics and Applications Pub Date : 2021-06-18 DOI: 10.54550/eca2021v1s3r23
S. Mukherjee, S. Mukherjee
{"title":"Counting on matrices","authors":"S. Mukherjee, S. Mukherjee","doi":"10.54550/eca2021v1s3r23","DOIUrl":"https://doi.org/10.54550/eca2021v1s3r23","url":null,"abstract":"In this paper, we have found formulas for the number of rectangular and symmetric matrices with the line sums divisible by a given integer. As an application, we have derived an explicit formula enumerating the number of traceless n × n, (0,1) symmetric matrices having line sums divisible by a given integer, which leads to an enumeration of labeled regular graphs with n vertices. Also, we have found a formula for the weighted enumerator (in terms of rows and columns) of rectangular matrices, which subsequently yields some nice identities satisfying curious reciprocity phenomena.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115883456","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 view from the bridge spanning combinatorics and probability 从桥的观点跨越组合和概率
Enumerative Combinatorics and Applications Pub Date : 2021-05-28 DOI: 10.54550/eca2021v1s3s3
R. Pinsky
{"title":"A view from the bridge spanning combinatorics and probability","authors":"R. Pinsky","doi":"10.54550/eca2021v1s3s3","DOIUrl":"https://doi.org/10.54550/eca2021v1s3s3","url":null,"abstract":"This paper presents an offering of some of the myriad connections between Combinatorics and Probability, directed in particular toward combinatorialists. The choice of material was dictated by the author’s own interests, tastes, and familiarity, as well as by a desire to present results with either complete proofs or well-developed sketches of proofs, and to ensure that the arguments are rather accessible to combinatorialists. The first several sections collect some concepts and rudimentary results from probability theory that are needed to understand the rest of the paper. 2020 Mathematics Subject Classification: 05-02; 60C05","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116938149","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: 2
Interview with Jeffrey Shallit 采访杰弗里·沙利特
Enumerative Combinatorics and Applications Pub Date : 2021-05-15 DOI: 10.54550/eca2022v2s2i5
Eça
{"title":"Interview with Jeffrey Shallit","authors":"Eça","doi":"10.54550/eca2022v2s2i5","DOIUrl":"https://doi.org/10.54550/eca2022v2s2i5","url":null,"abstract":"","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115024174","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
Lattice walks ending on a coordinate hyperplane avoiding backtracking and repeats 点阵行走结束于一个坐标超平面，避免回溯和重复
Enumerative Combinatorics and Applications Pub Date : 2021-05-06 DOI: 10.54550/ECA2022V2S1R3
John M. Machacek
{"title":"Lattice walks ending on a coordinate hyperplane avoiding backtracking and repeats","authors":"John M. Machacek","doi":"10.54550/ECA2022V2S1R3","DOIUrl":"https://doi.org/10.54550/ECA2022V2S1R3","url":null,"abstract":"We work with lattice walks in $mathbb{Z}^{r+1}$ using step set ${pm 1}^{r+1}$ that finish with $x_{r+1} = 0$. We further impose conditions of avoiding backtracking (i.e. $[v,-v]$) and avoiding consecutive steps (i.e. $[v,v]$) each possibly combined with restricting to the half-space $x_{r+1} geq 0$. We find in all cases the generating functions for such walks are algebraic and give explicit formulas for them. We also find polynomial recurrences for their coefficients. From the generating functions we find the asymptotic enumeration of each family of walks considered. The enumeration in special cases includes central binomial coefficients and Catalan numbers as well as relations to enumeration of another family of walks previously studied for which we provide bijection.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124811684","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
The mathematical life of Pierre Leroux 皮埃尔·勒鲁的数学生涯
Enumerative Combinatorics and Applications Pub Date : 2021-04-30 DOI: 10.54550/eca2021v1s3h3
G. Labelle
{"title":"The mathematical life of Pierre Leroux","authors":"G. Labelle","doi":"10.54550/eca2021v1s3h3","DOIUrl":"https://doi.org/10.54550/eca2021v1s3h3","url":null,"abstract":"","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130486212","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 the sparseness of the downsets of permutations via their number of separators 通过分隔符的数目来研究排列下集的稀疏性
Enumerative Combinatorics and Applications Pub Date : 2021-04-30 DOI: 10.54550/eca2021v1s3r21
Eli Bagno, E. Eisenberg, S. Reches, Moriah Sigron
{"title":"On the sparseness of the downsets of permutations via their number of separators","authors":"Eli Bagno, E. Eisenberg, S. Reches, Moriah Sigron","doi":"10.54550/eca2021v1s3r21","DOIUrl":"https://doi.org/10.54550/eca2021v1s3r21","url":null,"abstract":"Conventionally, a pair (σi, σi+1) is a bond in a permutation σ = σ1σ2 · · ·σn if σi− σi+1 = ±1. The number of bonds in a permutation σ ∈ Sn has a direct influence on the number of distinct patterns of order n − 1 contained in σ, affecting the structure of the downset of σ in the containment poset ⋃ n∈N Sn. Thus, to characterize the sparseness of the downset of a permutation σ ∈ Sn, we aim not only to find the number of bonds in σ, but also to predict the number of bonds contained in its patterns. To this end, we introduce a new statistic, separator number, as a significant factor in measuring the sparseness of this poset. An element σj in a permutation σ = σ1 · · ·σn ∈ Sn is defined to be a separator of σ if we can obtain a new bond by omitting it from σ. We also present some enumerative and asymptotic results regarding this new statistic.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128908113","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
Interview with Xavier Viennot 采访Xavier Viennot
Enumerative Combinatorics and Applications Pub Date : 2021-04-23 DOI: 10.54550/eca2022v2s1i4
Eça
{"title":"Interview with Xavier Viennot","authors":"Eça","doi":"10.54550/eca2022v2s1i4","DOIUrl":"https://doi.org/10.54550/eca2022v2s1i4","url":null,"abstract":"","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128563029","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
The convex hull of parking functions of length n 长度为n的停车函数的凸包
Enumerative Combinatorics and Applications Pub Date : 2021-04-17 DOI: 10.54550/ECA2022V2S2R10
Aruzhan Amanbayeva, Danielle Wang
{"title":"The convex hull of parking functions of length n","authors":"Aruzhan Amanbayeva, Danielle Wang","doi":"10.54550/ECA2022V2S2R10","DOIUrl":"https://doi.org/10.54550/ECA2022V2S2R10","url":null,"abstract":"Let Pn be the convex hull in R of all parking functions of length n. Stanley found the number of vertices and the number of facets of Pn. Building upon these results, we determine the number of faces of arbitrary dimension, the volume, and the number of integer points of Pn.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130633961","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: 8
Pattern avoidance and dominating compositions 模式回避和主导构图
Enumerative Combinatorics and Applications Pub Date : 2021-04-15 DOI: 10.54550/eca2022v2s1r4
Krishna Menon, Anurag Singh
{"title":"Pattern avoidance and dominating compositions","authors":"Krishna Menon, Anurag Singh","doi":"10.54550/eca2022v2s1r4","DOIUrl":"https://doi.org/10.54550/eca2022v2s1r4","url":null,"abstract":"Jel'inek, Mansour, and Shattuck studied Wilf-equivalence among pairs of patterns of the form ${sigma,tau}$ where $sigma$ is a set partition of size $3$ with at least two blocks. They obtained an upper bound for the number of Wilf-equivalence classes for such pairs. We show that their upper bound is the exact number of equivalence classes, thus solving a problem posed by them.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125501297","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
Peaks are preserved under run-sorting 在运行排序下保留峰值
Enumerative Combinatorics and Applications Pub Date : 2021-04-09 DOI: 10.54550/eca2022v2s1r2
P. Alexandersson, O. Nabawanda
{"title":"Peaks are preserved under run-sorting","authors":"P. Alexandersson, O. Nabawanda","doi":"10.54550/eca2022v2s1r2","DOIUrl":"https://doi.org/10.54550/eca2022v2s1r2","url":null,"abstract":"We study a sorting procedure (run-sorting) on permutations, where runs are rearranged in lexicographic order. We describe a rather surprising bijection on permutations on length n, with the property that it sends the set of peak-values (also known as the pinnacle set) to the set of peak-values after run-sorting. We also prove that the expected number of descents in a permutation σ ∈ Sn after run-sorting is equal to (n−2)/3. Moreover, we provide a closed-form of the exponential generating function introduced by Nabawanda, Rakotondrajao, and Bamunoba in 2020, for the number of run-sorted permutations of [n], (RSP(n)) having k runs, which gives a new interpretation to the sequence http://oeis.org/A124324. We show that the descent generating polynomials, An(t) for RSP(n) are real rooted, and satisfy an interlacing property similar to that satisfied by the Eulerian polynomials. Finally, we study run-sorted binary words and compute the expected number of descents after run-sorting a binary word of length n.","PeriodicalId":340033,"journal":{"name":"Enumerative Combinatorics and Applications","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122214722","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: 2
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