Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities

被引：5

作者：

Mukherjee, Sajal Kumar ^{[1
]}

Bera, Sudip ^{[2
]}

机构：

[1] Visva Bharati, Dept Math, Santini Ketan 731235, W Bengal, India

[2] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

来源：

DISCRETE MATHEMATICS | 2019年 / 342卷 / 06期

关键词：

Determinants; Digraphs; Newton-Girard identity; Combinatorial proof;

D O I：

10.1016/j.disc.2019.02.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we give combinatorial proofs of some well known identities and obtain some generalizations. We give a visual proof of a result of Chapman and Costas-Santos regarding the determinant of sum of matrices. Also we find a new identity expressing the permanent of sum of matrices. Besides, we give a graph theoretic proof of the Newton Girard identity in a generalized form. (C) 2019 Elsevier B.V. All rights reserved.

引用

页码：1577 / 1580

页数：4