Symmetric functions in noncommuting variables in superspace

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-11-12 DOI:10.1016/j.disc.2024.114320

Diego Arcis , Camilo González , Sebastián Márquez

引用次数: 0

Abstract

In 2004, Rosas and Sagan developed the theory of symmetric functions in noncommuting variables, achieving results analogous to classical symmetric functions. On the other hand, the same year, Desrosiers, Lapointe and Mathieu introduced the theory of symmetric functions in superspace, involving both commuting and anticommuting variables, extending the classic theory. Here, we introduce symmetric functions in noncommuting variables in superspace. We extend the classical symmetric functions in noncommuting variables to superspace: monomial, power sum, elementary and complete homogeneous functions. These functions generalize both those studied by Rosas and Sagan and those studied by Desrosiers, Lapointe, and Mathieu. Additionally, we define Schur–type functions in noncommuting variables in superspace.

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超空间非交换变量中的对称函数

2004 年，罗萨斯和萨根发展了非交换变量中的对称函数理论，取得了与经典对称函数类似的结果。另一方面，同年，Desrosiers、Lapointe 和 Mathieu 引入了超空间对称函数理论，涉及交换变量和反交换变量，扩展了经典理论。在此，我们介绍超空间中非交换变量的对称函数。我们将经典的非交换变量对称函数扩展到超空间：单项式函数、幂和函数、初等函数和完全同调函数。这些函数既概括了罗萨斯和萨根研究的函数，也概括了德斯罗西耶、拉普安特和马修研究的函数。此外，我们还定义了超空间非交换变量中的舒尔型函数。

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.