Flows on simplicial complexes

Abstract

Given a graph G, the number of nowhere-zero ℤq-flows φG(q) is known to be a polynomial in q. We extend the definition of nowhere-zero ℤq-flows to simplicial complexes Δ of dimension greater than one, and prove the polynomiality of the corresponding function φΔ (q) for certain q and certain subclasses of simplicial complexes. © 2012 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.