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

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. © 2019 Elsevier B.V