一些与欧拉多项式和排列多项式有关的交错序列

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-05-28 DOI:10.1016/j.disc.2025.114598

Xue Yan, Lily Li Liu

{"title":"一些与欧拉多项式和排列多项式有关的交错序列","authors":"Xue Yan, Lily Li Liu","doi":"10.1016/j.disc.2025.114598","DOIUrl":null,"url":null,"abstract":"<div><div>The Eulerian polynomials and derangement polynomials arise often in combinatorics, algebra and geometry. It is well known that the Eulerian polynomials and derangement polynomials form generalized Sturm sequences, respectively. In this paper, we give new sufficient conditions for the interlacing property of recurrence sequences of polynomials. As applications, we show some interesting interlacing sequences among the Eulerian polynomials, the derangement polynomials and those generalized polynomials for colored permutations.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 11","pages":"Article 114598"},"PeriodicalIF":0.7000,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some interlacing sequences related to the Eulerian and derangement polynomials\",\"authors\":\"Xue Yan, Lily Li Liu\",\"doi\":\"10.1016/j.disc.2025.114598\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The Eulerian polynomials and derangement polynomials arise often in combinatorics, algebra and geometry. It is well known that the Eulerian polynomials and derangement polynomials form generalized Sturm sequences, respectively. In this paper, we give new sufficient conditions for the interlacing property of recurrence sequences of polynomials. As applications, we show some interesting interlacing sequences among the Eulerian polynomials, the derangement polynomials and those generalized polynomials for colored permutations.</div></div>\",\"PeriodicalId\":50572,\"journal\":{\"name\":\"Discrete Mathematics\",\"volume\":\"348 11\",\"pages\":\"Article 114598\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0012365X25002067\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X25002067","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

欧拉多项式和无序多项式经常出现在组合学、代数和几何中。众所周知，欧拉多项式和无序多项式分别形成广义Sturm序列。本文给出了多项式递归序列的交错性的新的充分条件。作为应用，我们给出了一些有趣的欧拉多项式、无序多项式和有色排列的广义多项式之间的交错序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Some interlacing sequences related to the Eulerian and derangement polynomials

The Eulerian polynomials and derangement polynomials arise often in combinatorics, algebra and geometry. It is well known that the Eulerian polynomials and derangement polynomials form generalized Sturm sequences, respectively. In this paper, we give new sufficient conditions for the interlacing property of recurrence sequences of polynomials. As applications, we show some interesting interlacing sequences among the Eulerian polynomials, the derangement polynomials and those generalized polynomials for colored permutations.

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

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.