Computing character tables and Cartan matrices of finite monoids with fixed point counting

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2024-07-20 DOI:10.1016/j.jsc.2024.102371

Balthazar Charles

引用次数: 0

Abstract

In this paper we present an algorithm for efficiently counting fixed points in a finite monoid M under a conjugacy-like action. We then prove a formula for the character table of M in terms of fixed points, which allows for the effective computation of both the character table of M other a field of null characteristic, as well as its Cartan matrix, using a formula from [Thiéry '12], again in terms of fixed points. We discuss the implementation details of the resulting algorithms and provide benchmarks of their performance.

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用定点计数计算有限单体的字符表和卡坦矩阵

在本文中，我们提出了一种在共轭样作用下有效计算有限单元中定点的算法。然后，我们证明了一个以定点为单位的特征表公式，它允许使用[Thiéry'12]中的公式，同样以定点为单位，有效计算其他空特征域的特征表及其笛卡尔矩阵。我们将讨论由此产生的算法的实现细节，并提供其性能基准。

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

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.