Inductive Proof of Borchardt's Theorem
Chemical Physics
2023-09-13 v1
Abstract
We provide an inductive proof of Borchardt's theorem for calculating the permanent of a Cauchy matrix via the determinants of auxiliary matrices. This result has implications for antisymmetric products of interacting geminals (APIG), and suggests that the restriction of the APIG coefficients to Cauchy form (typically called APr2G) is special in its tractability.
Cite
@article{arxiv.2309.05886,
title = {Inductive Proof of Borchardt's Theorem},
author = {Andy A. Chavez and Alec P. Adam and Paul W. Ayers and Ramón Alain Miranda-Quintana},
journal= {arXiv preprint arXiv:2309.05886},
year = {2023}
}