零永久的4阶多随机矩阵的表征

IF 1.2 2区数学 Q2 MATHEMATICS

Journal of Combinatorial Theory Series A Pub Date : 2025-04-30 DOI:10.1016/j.jcta.2025.106060

Aleksei L. Perezhogin , Vladimir N. Potapov , Anna A. Taranenko , Sergey Yu. Vladimirov

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引用次数: 0

摘要

一个多维非负矩阵，如果其每一行上的元素之和等于1，则称为多随机矩阵。多维矩阵的恒量是所有对角线上元素的乘积的和。证明了如果d是偶数，则4阶的d维多随机矩阵的永久性是正的，对于奇数d，我们给出了零永久性的d维多随机矩阵的完整刻画。

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Characterization of polystochastic matrices of order 4 with zero permanent

A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to 1. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if d is even, then the permanent of a d-dimensional polystochastic matrix of order 4 is positive, and for odd d, we give a complete characterization of d-dimensional polystochastic matrices with zero permanent.

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来源期刊

Journal of Combinatorial Theory Series A 数学-数学

CiteScore

2.90

自引率

9.10%

发文量

审稿时长

12 months

期刊介绍： The Journal of Combinatorial Theory publishes original mathematical research concerned with theoretical and physical aspects of the study of finite and discrete structures in all branches of science. Series A is concerned primarily with structures, designs, and applications of combinatorics and is a valuable tool for mathematicians and computer scientists.