关于最小永久点的猜想

IF 0.4 4区数学 Q4 MATHEMATICS Czechoslovak Mathematical Journal Pub Date : 2023-12-11 DOI:10.21136/cmj.2023.0186-23

Gi-Sang Cheon, Seok-Zun Song

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引用次数: 0

摘要

考虑一类双随机矩阵多面体面上的永久函数，这些矩阵的非零项与包含单位子矩阵的完全不可分解的正方形(0,1)矩阵的非零项重合。我们通过确定双随机矩阵多面体的某些面上的最小永久值，证明了K. Pula, S. Z. Song, I. M. Wanless(2011)中的一个猜想在某些情况下是正确的。

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A conjecture on minimum permanents

We consider the permanent function on the faces of the polytope of certain doubly stochastic matrices, whose nonzero entries coincide with those of fully indecomposable square (0, 1)-matrices containing the identity submatrix. We show that a conjecture in K. Pula, S. Z. Song, I. M. Wanless (2011), is true for some cases by determining the minimum permanent on some faces of the polytope of doubly stochastic matrices.

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