A Multiset Version of Even-Odd Permutations Identity

TL;DR

This paper presents a new bijective proof of a multiset extension of the even-odd permutations identity, linking combinatorial permutation theory to statistical physics models.

Contribution

It introduces a novel bijective proof for a multiset version of the identity, connecting combinatorics with physical models like the Ising model.

Findings

Establishes a bijective proof for the multiset analogue of the identity.

Links the combinatorial lemma to Feynman's conjecture on planar graph paths.

Provides insights into combinatorial structures underlying statistical physics models.

Abstract

In this paper, we give a new bijective proof of a multiset analogue of even-odd permutations identity. This multiset version is equivalent to the original coin arrangements lemma which is a key combinatorial lemma in the Sherman's Proof of a conjecture of Feynman about an identity on paths in planar graphs related to combinatorial solution of two dimensional Ising model in statistical physics.