### Flows on Simplicial Complexes

*Matthias Beck, Yvonne Kemper*

#### 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.

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