Year: 2024
Type: article
Abstract: A regular matroid M on a finite set E is represented by a totally unimodular matrix. The set of vectors from ZE orthogonal to rows of the matrix form a regular chain group N. Assume that ψ is a homomorphism from N into a finite additive Abelian group A and let Aψ[N] be the set of vectors g from (A−0)E, such that ∑e∈Eg(e)·f(e)=ψ(f) for each f∈N (where · is a scalar multiplication). We show that |Aψ[N]| can be evaluated by a polynomial function of |A|. In particular, if ψ(f)=0 for each f∈N, then the corresponding assigning polynomial is the classical characteristic polynomial of M.
Source: Mathematics
DOI: 10.3390/math12203218
Author: Martin Kochol
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4403389910