Combinatorial proofs of the Newton-Girard and Chapman-Costas-Santos identities
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2018
- DOI:
- 10.48550/arXiv.1807.11749
- arXiv:
- arXiv:1807.11749
- Bibcode:
- 2018arXiv180711749M
- Keywords:
-
- Mathematics - Combinatorics;
- 05A19;
- 05A05;
- 05C30;
- 05C38
- E-Print:
- 6 pages, 1 figure