Polynomials Counting Nowhere-Zero Chains Associated with Homomorphisms

Martin Kochol ()
Additional contact information
Martin Kochol: Mathematical Institute, Slovak Academy od Sciences, 814 73 Bratislava, Slovakia

Mathematics, 2024, vol. 12, issue 20, 1-11

Abstract: A regular matroid M on a finite set E is represented by a totally unimodular matrix. The set of vectors from Z E 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 A ψ [ N ] be the set of vectors g from ( A − 0 ) E , such that ∑ e ∈ E g ( e ) · f ( e ) = ψ ( f ) for each f ∈ N (where · is a scalar multiplication). We show that | A ψ [ 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 .

Keywords: regular matroid; regular chain group; totally unimodular matrix; homomorphism; assigning polynomial (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/20/3218/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/20/3218/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:20:p:3218-:d:1498656

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().