Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities
Sajal Kumar Mukherjee, Sudip Bera
TL;DR
This paper provides combinatorial and visual proofs for classical identities like Newton-Girard and Chapman-Costas-Santos, introduces generalizations, and offers new insights into matrix determinants and permanents.
Contribution
It presents novel combinatorial proofs, generalizations of known identities, and a graphical interpretation of the Newton-Girard identity.
Findings
Combinatorial proofs of classical identities
A new identity for the permanent of sum of matrices
Graphical interpretation of Newton-Girard identity
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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