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

Sajal Kumar Mukherjee,Sudip Bera

doi:10.1016/j.disc.2019.02.013

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

Sajal Kumar Mukherjee, Sudip Bera

Open Access

https://doi.org/10.1016/j.disc.2019.02.013

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Journal: Discrete Mathematics	Publication Date: Mar 11, 2019
Citations: 8	License type: publisher-specific-oa

Affiliation: Indian Institute of Science Bangalore

#Generalized Form #Graph Theoretic Proof + Show 4 more

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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 the permanent of sum of matrices. Besides, we give a graph theoretic proof of the Newton–Girard identity in a generalized form.

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