Noncommutative symmetric functions and skewing operators

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-09-10 DOI:10.1016/j.disc.2024.114255

引用次数: 0

Abstract

Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying expansions of a given symmetric function in terms of various bases. In this paper, we establish a further development of the theory for studying skewing operators. Using this machinery, we are able to easily reproduce the Littlewood–Richardson rule and provide recurrence relations for chromatic quasisymmetric functions, which generalize Harada–Precup's recurrence.

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非交换对称函数和偏斜算子

由于对称函数空间乘积结构的重要性，偏斜算子在对称函数理论中发挥着核心作用。非交换对称函数理论是研究给定对称函数在各种基上展开的有用工具。在本文中，我们进一步发展了研究偏斜算子的理论。利用这一机制，我们能够轻松地重现 Littlewood-Richardson 规则，并提供色度准对称函数的递推关系，这是对 Harada-Precup 递推关系的概括。

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.