The extra basis in noncommuting variables

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2025-04-04 DOI:10.1016/j.aam.2025.102887

Farid Aliniaeifard, Stephanie van Willigenburg

引用次数: 0

Abstract

We answer a question of Bergeron, Hohlweg, Rosas, and Zabrocki from 2006 to give a combinatorial description for the coproduct of the x-basis in the Hopf algebra of symmetric functions in noncommuting variables, NCSym, which arises in the theory of Grothendieck bialgebras. We achieve this by applying the theory of Hopf monoids and the Fock functor. We also determine combinatorial expansions of this basis in terms of the monomial and power sum symmetric functions in NCSym, and by taking the commutative image of the x-basis we discover a new multiplicative basis for the algebra of symmetric functions.

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非交换变量的额外基

我们回答了Bergeron， Hohlweg, Rosas， and Zabrocki从2006年提出的一个问题，给出了非交换变量NCSym对称函数的Hopf代数中x基的余积的组合描述，该问题出现在Grothendieck双代数理论中。我们利用Hopf半群理论和Fock函子实现了这一点。我们还用NCSym中的单项式和幂和对称函数确定了该基的组合展开式，并通过取x基的交换像发现了对称函数代数的一种新的乘法基。

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

Advances in Applied Mathematics 数学-应用数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

85 days

期刊介绍： Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.