The Miracle of Integer Eigenvalues

IF 0.6 4区数学 Q3 MATHEMATICS

Functional Analysis and Its Applications Pub Date : 2024-07-21 DOI:10.1134/s0016266324020072

Richard Kenyon, Maxim Kontsevich, Oleg Ogievetskii, Cosmin Pohoata, Will Sawin, Semen Shlosman

引用次数: 0

Abstract

For partially ordered sets \((X, \preccurlyeq)\), we consider the square matrices \(M^{X}\) with rows and columns indexed by linear extensions of the partial order on \(X\). Each entry \((M^{X})_{PQ}\) is a formal variable defined by a pedestal of the linear order \(Q\) with respect to linear order \(P\). We show that all eigenvalues of any such matrix \(M^{X}\) are \(\mathbb{Z}\)-linear combinations of those variables.

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整数特征值的奇迹

摘要对于部分有序集 \((X,\preccurlyeq)\)，我们考虑方阵 \(M^{X}\)，其行和列以 \(X\)上部分有序的线性扩展为索引。每个条目 \((M^{X})_{PQ}\)都是由线性阶 \(Q\)的基座相对于线性阶 \(P\)定义的形式变量。我们证明任何这样的矩阵 \(M^{X}\) 的所有特征值都是（\mathbb{Z}\）这些变量的线性组合。

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

Functional Analysis and Its Applications 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.