A Multiset Version of Even-Odd Permutations Identity
This work addresses a combinatorial problem in statistical physics, but it is incremental as it provides a new proof for an existing lemma without introducing new methods or results.
The paper presents a new bijective proof for a multiset analogue of the even-odd permutations identity, which is equivalent to the coin arrangements lemma used in Sherman's proof of a Feynman conjecture related to the two-dimensional Ising model in statistical physics.
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.