关于Tutte多项式的相容集展开

IF 0.6 4区 数学 Q4 MATHEMATICS, APPLIED Annals of Combinatorics Pub Date : 2023-06-30 DOI:10.1007/s00026-023-00657-z
Laura Pierson
{"title":"关于Tutte多项式的相容集展开","authors":"Laura Pierson","doi":"10.1007/s00026-023-00657-z","DOIUrl":null,"url":null,"abstract":"<div><p>Kochol [6] gave a new expansion formula for the Tutte polynomial of a matroid using the notion of <i>compatible sets</i>, and asked how this expansion relates to the internal-external activities formula. Here, we provide an answer, which is obtained as a special case of a generalized version of the expansion formula to Las Vergnas’s trivariate Tutte polynomials of matroid perspectives [10]. The same generalization to matroid perspectives and bijection with activities have been independently proven by Kochol in [5] and [7] in parallel with this work, but using different methods. Kochol proves both results recursively using the contraction-deletion relations, whereas we give a more direct proof of the bijection and use that to deduce the compatible sets expansion formula from Las Vergnas’s activities expansion.</p></div>","PeriodicalId":50769,"journal":{"name":"Annals of Combinatorics","volume":"28 1","pages":"33 - 42"},"PeriodicalIF":0.6000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Compatible Sets Expansion of the Tutte Polynomial\",\"authors\":\"Laura Pierson\",\"doi\":\"10.1007/s00026-023-00657-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Kochol [6] gave a new expansion formula for the Tutte polynomial of a matroid using the notion of <i>compatible sets</i>, and asked how this expansion relates to the internal-external activities formula. Here, we provide an answer, which is obtained as a special case of a generalized version of the expansion formula to Las Vergnas’s trivariate Tutte polynomials of matroid perspectives [10]. The same generalization to matroid perspectives and bijection with activities have been independently proven by Kochol in [5] and [7] in parallel with this work, but using different methods. Kochol proves both results recursively using the contraction-deletion relations, whereas we give a more direct proof of the bijection and use that to deduce the compatible sets expansion formula from Las Vergnas’s activities expansion.</p></div>\",\"PeriodicalId\":50769,\"journal\":{\"name\":\"Annals of Combinatorics\",\"volume\":\"28 1\",\"pages\":\"33 - 42\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Combinatorics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00026-023-00657-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Combinatorics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00026-023-00657-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

摘要

Kochol [6]利用兼容集的概念给出了矩阵的 Tutte 多项式的新展开式,并提出了这一展开式与内部-外部活动式之间的关系。在这里,我们给出了答案,它是 Las Vergnas 的矩阵视角三变量 Tutte 多项式的扩展公式的广义版本的特例[10]。与这项工作平行,Kochol 在 [5] 和 [7] 中独立证明了对 matroid 透视图的相同广义化和与活动的双射,但使用的方法不同。Kochol 利用收缩-删除关系递归证明了这两个结果,而我们则更直接地证明了双射,并利用双射从 Las Vergnas 的活动展开推导出了兼容集展开公式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

摘要图片

摘要图片

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
On the Compatible Sets Expansion of the Tutte Polynomial

Kochol [6] gave a new expansion formula for the Tutte polynomial of a matroid using the notion of compatible sets, and asked how this expansion relates to the internal-external activities formula. Here, we provide an answer, which is obtained as a special case of a generalized version of the expansion formula to Las Vergnas’s trivariate Tutte polynomials of matroid perspectives [10]. The same generalization to matroid perspectives and bijection with activities have been independently proven by Kochol in [5] and [7] in parallel with this work, but using different methods. Kochol proves both results recursively using the contraction-deletion relations, whereas we give a more direct proof of the bijection and use that to deduce the compatible sets expansion formula from Las Vergnas’s activities expansion.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Annals of Combinatorics
Annals of Combinatorics 数学-应用数学
CiteScore
1.00
自引率
0.00%
发文量
56
审稿时长
>12 weeks
期刊介绍: Annals of Combinatorics publishes outstanding contributions to combinatorics with a particular focus on algebraic and analytic combinatorics, as well as the areas of graph and matroid theory. Special regard will be given to new developments and topics of current interest to the community represented by our editorial board. The scope of Annals of Combinatorics is covered by the following three tracks: Algebraic Combinatorics: Enumerative combinatorics, symmetric functions, Schubert calculus / Combinatorial Hopf algebras, cluster algebras, Lie algebras, root systems, Coxeter groups / Discrete geometry, tropical geometry / Discrete dynamical systems / Posets and lattices Analytic and Algorithmic Combinatorics: Asymptotic analysis of counting sequences / Bijective combinatorics / Univariate and multivariable singularity analysis / Combinatorics and differential equations / Resolution of hard combinatorial problems by making essential use of computers / Advanced methods for evaluating counting sequences or combinatorial constants / Complexity and decidability aspects of combinatorial sequences / Combinatorial aspects of the analysis of algorithms Graphs and Matroids: Structural graph theory, graph minors, graph sparsity, decompositions and colorings / Planar graphs and topological graph theory, geometric representations of graphs / Directed graphs, posets / Metric graph theory / Spectral and algebraic graph theory / Random graphs, extremal graph theory / Matroids, oriented matroids, matroid minors / Algorithmic approaches
期刊最新文献
Orientable Vertex Primitive Complete Maps Publisher Correction to: An Asymptotic Lower Bound on the Number of Polyominoes Efficient Representation of Lattice Path Matroids Partitions with Fixed Points in the Sequence of First-Column Hook Lengths Acyclic Reorientation Lattices and Their Lattice Quotients
×
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
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1