Enumeration of weighted paths on a digraph and block hook determinant

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2019-12-03 DOI:10.1515/spma-2020-0130

S. Bera

引用次数: 1

Abstract

Abstract In this article, we evaluate determinants of “block hook” matrices, which are block matrices consist of hook matrices. In particular, we deduce that the determinant of a block hook matrix factorizes nicely. In addition we give a combinatorial interpretation of the aforesaid factorization property by counting weighted paths in a suitable weighted digraph.

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有向图上加权路径的计数与块钩行列式

摘要本文讨论了“块-钩”矩阵的行列式，它是由钩矩阵组成的块矩阵。特别地，我们推导出块钩矩阵的行列式可以很好地因子分解。此外，我们通过在适当的加权有向图中计数加权路径，给出了上述因子分解性质的组合解释。

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

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.