Interlacing property of polynomial sequences related to multinomial coefficients

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-05 DOI:10.1016/j.disc.2025.114522

Ming-Jian Ding

引用次数: 0

Abstract

In this paper, we show that several consecutive generating functions of the multinomial coefficients form an interlacing sequence. As applications, we provide a positive response to a question proposed by Fisk regarding the interlacing property for zeros of polynomials, which are generated by the central trinomial (quadrinomial) coefficients.

Furthermore, we prove that some classical polynomial sequences also possess the interlacing property. These sequences include the (weak) exceedance polynomial sequence on involutions in the symmetric group, Motzkin polynomial sequence, local h-polynomial sequences of the cluster subdivision of Cartan-Killing types A, B and D, Narayana polynomial sequences of types A and B, and others.

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与多项系数相关的多项式序列的隔行性

本文证明了若干项系数的连续生成函数构成了一个交错序列。作为应用，我们对Fisk提出的关于由中心三项式（四项）系数产生的多项式的零的隔行性的问题提供了积极的响应。进一步证明了一些经典多项式序列也具有隔行性。这些序列包括对称群对合上的（弱）超越多项式序列、Motzkin多项式序列、Cartan-Killing类型A、B和D的聚类细分的局部h-多项式序列、A和B类型的Narayana多项式序列等。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.