扩展舒尔函数和渐开线相关基数

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics Pub Date : 2024-09-03 DOI:10.1016/j.aam.2024.102770

Spencer Daugherty

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引用次数: 0

摘要

我们引入了 QSym 的两个新基，即反向扩展舒尔函数和行严格反向扩展舒尔函数，以及它们在 NSym 中的对偶基，即反向歆函数和行严格反向歆函数。这些基是扩展舒尔基和胫基在卷积 ρ 和 ω 下的映像，而卷积 ρ 和 ω 是对称函数上经典卷积 ω 的一般化。此外，我们还利用创造算子证明了某些歆函数的雅各比-特鲁迪法则。我们分别基于 NSym 和 QSym 的左作用和右作用定义了偏斜扩展舒尔函数和偏斜-II 扩展舒尔函数。然后，我们使用渐开线 ρ 和 ω 将这些结果和其他已知结果转化为我们的反向基和行严格反向基。

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Extended Schur functions and bases related by involutions

We introduce two new bases of $Q S y m$ , the reverse extended Schur functions and the row-strict reverse extended Schur functions, as well as their duals in NSym, the reverse shin functions and row-strict reverse shin functions. These bases are the images of the extended Schur basis and shin basis under the involutions ρ and ω, which generalize the classical involution ω on the symmetric functions. In addition, we prove a Jacobi-Trudi rule for certain shin functions using creation operators. We define skew extended Schur functions and skew-II extended Schur functions based on left and right actions of NSym and $Q S y m$ respectively. We then use the involutions ρ and ω to translate these and other known results to our reverse and row-strict reverse bases.

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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.