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

2018/07/31 by Sajal Kumar Mukherjee, Mukherjee, Sajal Kumar, Sudip Bera +1
Mathematics · #05A05 #05A19 #05C30 #05C38 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A19 #msc:05C30 #msc:05C38

paper · pdf · doi:10.48550/arxiv.1807.11749

6 pages, 1 figure

arxiv created 2018/10/09 · arxiv updated 2018/10/10

Abstract

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 permanent of sum of matrices. Besides, we give a graphical interpretation of Newton-Girard identity.

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