A Determinantal Identity for the Permanent of a Rank 2 Matrix
Combinatorics
2021-08-11 v2
Abstract
We prove an identity relating the permanent of a rank matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that these are actually special cases of some more general identity (or class of identities) connecting permanents and determinants. The proof combines some basic facts from the theory of symmetric functions with an application of a famous theorem of Binet and Cauchy in linear algebra.
Keywords
Cite
@article{arxiv.2108.02528,
title = {A Determinantal Identity for the Permanent of a Rank 2 Matrix},
author = {Adam W. Marcus},
journal= {arXiv preprint arXiv:2108.02528},
year = {2021}
}