Generalized Schröder paths arising from a combinatorial interpretation of generalized Laurent bi-orthogonal polynomials

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-10 DOI:10.1016/j.disc.2024.114230

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引用次数: 0

Abstract

Lattice paths called ℓ-Schröder paths are introduced. They are paths on the upper half-plane consisting of $ℓ + 2$ types of steps: $(i, ℓ - i)$ for $i = 0, \dots, ℓ$ , and $(1, - 1)$ . Those paths generalize Schröder paths and some variants, such as m-Schröder paths by Yang and Jiang and Motzkin-Schröder paths by Kim and Stanton. We show that ℓ-Schröder paths arise naturally from a combinatorial interpretation of the moments of generalized Laurent bi-orthogonal polynomials introduced by Wang, Chang, and Yue. We also show that some generating functions of non-intersecting ℓ-Schröder paths can be factorized in closed forms.

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广义劳伦双正交多项式的组合解释所产生的广义施罗德路径

引入了称为 ℓ-Schröder 路径的网格路径。它们是由 ℓ+2 种步长组成的上半平面路径：i=0,...,ℓ时的(i,ℓ-i)和(1,-1)。这些路径概括了施罗德路径和一些变体，例如杨和江的 m-Schröder 路径以及金和斯坦顿的 Motzkin-Schröder 路径。我们证明，ℓ-Schröder 路径自然产生于对王、张和岳提出的广义劳伦特双正交多项式矩的组合解释。我们还证明了一些非相交ℓ-Schröder 路径的生成函数可以用封闭形式因式分解。

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.