发布求助
文献互助 智能选刊 最新文献

Journal of Algebraic Combinatorics最新文献

筛选
英文 中文
The Ariki–Koike algebras and Rogers–Ramanujan type partitions 有熊小池代数和罗杰斯-拉马努扬类型分区
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-31 DOI: 10.1007/s10801-024-01340-z
Shane Chern, Zhitai Li, Dennis Stanton, Ting Xue, Ae Ja Yee
{"title":"The Ariki–Koike algebras and Rogers–Ramanujan type partitions","authors":"Shane Chern, Zhitai Li, Dennis Stanton, Ting Xue, Ae Ja Yee","doi":"10.1007/s10801-024-01340-z","DOIUrl":"https://doi.org/10.1007/s10801-024-01340-z","url":null,"abstract":"<p>Ariki and Mathas (Math Z 233(3):601–623, 2000) showed that the simple modules of the Ariki–Koike algebras <span>(mathcal {H}_{mathbb {C},v;Q_1,ldots , Q_m}big (G(m, 1, n)big ))</span> (when the parameters are roots of unity and <span>(v ne 1)</span>) are labeled by the so-called Kleshchev multipartitions. This together with Ariki’s categorification theorem enabled Ariki and Mathas to obtain the generating function for the number of Kleshchev multipartitions by making use of the Weyl–Kac character formula. In this paper, we revisit their generating function relation for the <span>(v=-1)</span> case. In particular, this <span>(v=-1)</span> scenario is of special interest as the corresponding Kleshchev multipartitions are closely tied with generalized Rogers–Ramanujan type partitions when <span>(Q_1=cdots =Q_a=-1)</span> and <span>(Q_{a+1}=cdots =Q_m =1)</span>. Based on this connection, we provide an analytic proof of the result of Ariki and Mathas for the above choice of parameters. Our second objective is to investigate simple modules of the Ariki–Koike algebra in a fixed block, which are, as widely known, labeled by the Kleshchev multiparitions with a fixed partition residue statistic. This partition statistic is also studied in the works of Berkovich, Garvan, and Uncu. Employing their results, we provide two bivariate generating function identities for the <span>(m=2)</span> scenario.\u0000</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141195403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Growth of bilinear maps II: bounds and orders 双线性映射的增长 II：边界和阶数
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-21 DOI: 10.1007/s10801-024-01336-9
Vuong Bui
{"title":"Growth of bilinear maps II: bounds and orders","authors":"Vuong Bui","doi":"10.1007/s10801-024-01336-9","DOIUrl":"https://doi.org/10.1007/s10801-024-01336-9","url":null,"abstract":"<p>A good range of problems on trees can be described by the following general setting: Given a bilinear map <span>(*:mathbb {R}^dtimes mathbb {R}^drightarrow mathbb {R}^d)</span> and a vector <span>(sin mathbb {R}^d)</span>, we need to estimate the largest possible absolute value <i>g</i>(<i>n</i>) of an entry over all vectors obtained from applying <span>(n-1)</span> applications of <span>(*)</span> to <i>n</i> instances of <i>s</i>. When the coefficients of <span>(*)</span> are nonnegative and the entries of <i>s</i> are positive, the value <i>g</i>(<i>n</i>) is known to follow a growth rate <span>(lambda =lim _{nrightarrow infty } root n of {g(n)})</span>. In this article, we prove that for such <span>(*)</span> and <i>s</i> there exist nonnegative numbers <span>(r,r')</span> and positive numbers <span>(a,a')</span> so that for every <i>n</i>, </p><span>$$begin{aligned} a n^{-r}lambda ^nle g(n)le a' n^{r'}lambda ^n. end{aligned}$$</span><p>While proving the upper bound, we actually also provide another approach in proving the limit <span>(lambda )</span> itself. The lower bound is proved by showing a certain form of submultiplicativity for <i>g</i>(<i>n</i>). Corollaries include a lower bound and an upper bound for <span>(lambda )</span>, which are followed by a good estimation of <span>(lambda )</span> when we have the value of <i>g</i>(<i>n</i>) for an <i>n</i> large enough.</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Eigenvalues of thick regular near hexagons 厚正则近六边形的特征值
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-21 DOI: 10.1007/s10801-024-01322-1
Akira Hiraki
{"title":"Eigenvalues of thick regular near hexagons","authors":"Akira Hiraki","doi":"10.1007/s10801-024-01322-1","DOIUrl":"https://doi.org/10.1007/s10801-024-01322-1","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141116058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 weak Lefschetz property and mixed multiplicities of monomial ideals 弱列夫谢茨性质和单项式理想的混合乘数
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-21 DOI: 10.1007/s10801-024-01337-8
Thiago Holleben
{"title":"The weak Lefschetz property and mixed multiplicities of monomial ideals","authors":"Thiago Holleben","doi":"10.1007/s10801-024-01337-8","DOIUrl":"https://doi.org/10.1007/s10801-024-01337-8","url":null,"abstract":"<p>Recently, H. Dao and R. Nair gave a combinatorial description of simplicial complexes <span>(Delta )</span> such that the squarefree reduction of the Stanley–Reisner ideal of <span>(Delta )</span> has the WLP in degree 1 and characteristic zero. In this paper, we apply the connections between analytic spread of equigenerated monomial ideals, mixed multiplicities and birational monomial maps to give a sufficient and necessary condition for the squarefree reduction <span>(A(Delta ))</span> to satisfy the WLP in degree <i>i</i> and characteristic zero in terms of mixed multiplicities of monomial ideals that contain combinatorial information of <span>(Delta )</span>, we call them incidence ideals. As a consequence, we give an upper bound to the possible failures of the WLP of <span>(A(Delta ))</span> in degree <i>i</i> in positive characteristics in terms of mixed multiplicities. Moreover, we extend Dao and Nair’s criterion to arbitrary monomial ideals in positive odd characteristics.</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Higher Bruhat orders of types B and C B 类和 C 类更高的布鲁哈特阶数
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-17 DOI: 10.1007/s10801-024-01334-x
Vladimir I. Danilov, Alexander V. Karzanov, Gleb A. Koshevoy
{"title":"Higher Bruhat orders of types B and C","authors":"Vladimir I. Danilov, Alexander V. Karzanov, Gleb A. Koshevoy","doi":"10.1007/s10801-024-01334-x","DOIUrl":"https://doi.org/10.1007/s10801-024-01334-x","url":null,"abstract":"<p>We propose versions of higher Bruhat orders for types <i>B</i> and <i>C</i>. This is based on a theory of higher Bruhat orders of type A and their geometric interpretations (due to Manin–Shekhtman, Voevodskii–Kapranov, and Ziegler), and on our study of the so-called symmetric cubillages of cyclic zonotopes.\u0000</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Nowhere-zero 3-flows in nilpotently vertex-transitive graphs 无顶点遍历图中的无处-零3流
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-16 DOI: 10.1007/s10801-024-01335-w
Junyang Zhang, Sanming Zhou
{"title":"Nowhere-zero 3-flows in nilpotently vertex-transitive graphs","authors":"Junyang Zhang, Sanming Zhou","doi":"10.1007/s10801-024-01335-w","DOIUrl":"https://doi.org/10.1007/s10801-024-01335-w","url":null,"abstract":"<p>We prove that every regular graph of valency at least four whose automorphism group contains a nilpotent subgroup acting transitively on the vertex set admits a nowhere-zero 3-flow.\u0000</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Construction of cospectral graphs, signed graphs and $${mathbb {T}}$$-gain graphs via partial transpose 通过部分转置构建余谱图、有符号图和 $${mathbb {T}}$ 增益图
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-16 DOI: 10.1007/s10801-024-01332-z
Francesco Belardo, Maurizio Brunetti, Matteo Cavaleri, Alfredo Donno
{"title":"Construction of cospectral graphs, signed graphs and $${mathbb {T}}$$-gain graphs via partial transpose","authors":"Francesco Belardo, Maurizio Brunetti, Matteo Cavaleri, Alfredo Donno","doi":"10.1007/s10801-024-01332-z","DOIUrl":"https://doi.org/10.1007/s10801-024-01332-z","url":null,"abstract":"","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140971050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Counting and signed counting permutations by descent-based statistics 基于后裔统计的计数和符号计数排列
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-09 DOI: 10.1007/s10801-024-01330-1
Yao Dong, Zhicong Lin
{"title":"Counting and signed counting permutations by descent-based statistics","authors":"Yao Dong, Zhicong Lin","doi":"10.1007/s10801-024-01330-1","DOIUrl":"https://doi.org/10.1007/s10801-024-01330-1","url":null,"abstract":"<p>The original motivation of this paper was to find the context-free grammar for the joint distribution of peaks and valleys on permutations. Although such attempt was unsuccessful, we can obtain noncommutative symmetric function identities for the joint distributions of several descent-based statistics, including peaks, valleys and even/odd descents, on permutations via Zhuang’s generalized run theorem. Our results extend in a unified way several generating function formulas exist in the literature, including formulas of Carlitz and Scoville (Discrete Math 5:45–59, 1973; J Reine Angew Math 265:110–137, 1974), J. Combin. Theory Ser. A, 20: 336-356 (1976), Zhuang (Adv Appl Math 90:86–144, 2017), Pan and Zeng (Adv Appl Math 104:85–99, 2019; Discrete Math 346:113575, 2023). As applications of these generating function formulas, Wachs’ involution and Foata–Strehl action on permutations, we also investigate the signed counting of even and odd descents, and of descents and peaks, which provide two generalizations of Désarménien and Foata’s classical signed Eulerian identity.</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 cyclic flats of a q-matroid q-matroid 的循环平面
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-09 DOI: 10.1007/s10801-024-01321-2
Gianira N. Alfarano, Eimear Byrne
{"title":"The cyclic flats of a q-matroid","authors":"Gianira N. Alfarano, Eimear Byrne","doi":"10.1007/s10801-024-01321-2","DOIUrl":"https://doi.org/10.1007/s10801-024-01321-2","url":null,"abstract":"<p>In this paper we develop the theory of cyclic flats of <i>q</i>-matroids. We show that the cyclic flats, together with their ranks, uniquely determine a <i>q</i>-matroid and hence derive a new <i>q</i>-cryptomorphism. We introduce the notion of <span>(mathbb {F}_{q^m})</span>-independence of an <span>(mathbb {F}_q)</span>-subspace of <span>(mathbb {F}_q^n)</span> and we show that <i>q</i>-matroids generalize this concept, in the same way that matroids generalize the notion of linear independence of vectors over a given field.\u0000</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Intersection bodies of polytopes: translations and convexity 多边形的交点体：平移和凸性
IF 0.8 3区 数学
Journal of Algebraic Combinatorics Pub Date : 2024-05-09 DOI: 10.1007/s10801-024-01328-9
Marie-Charlotte Brandenburg, Chiara Meroni
{"title":"Intersection bodies of polytopes: translations and convexity","authors":"Marie-Charlotte Brandenburg, Chiara Meroni","doi":"10.1007/s10801-024-01328-9","DOIUrl":"https://doi.org/10.1007/s10801-024-01328-9","url":null,"abstract":"<p>We continue the study of intersection bodies of polytopes, focusing on the behavior of <i>IP</i> under translations of <i>P</i>. We introduce an affine hyperplane arrangement and show that the polynomials describing the boundary of <span>(I(P+t))</span> can be extended to polynomials in variables <span>(tin mathbb {R}^d)</span> within each region of the arrangement. In dimension 2, we give a full characterization of those polygons such that their intersection body is convex. We give a partial characterization for general dimensions.</p>","PeriodicalId":14926,"journal":{"name":"Journal of Algebraic Combinatorics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140939854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信