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Flows on Simplicial Complexes

By Matthias Beck and 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 ∆ of dimension greater than one, and prove the polynomiality of the corresponding function φ∆(q) for certain q and certain subclasses of simplicial complexes. Résumé. E´tant donné une graphe G, on est connu que le nombre de Zq-flots non-nuls G (q) est un polynˆome dans q. Nous étendons la définition de Zq-flots non-nuls pour incluir des complexes simpliciaux de dimension plus grande qu’un, et on montre que le nombre est aussi un polynˆome de la fonction correspondante pour certain valeurs de q et de certaines sous-classes de complexes simpliciaux

Topics: Nowhere-zero flows, simplicial complexes, matroids, Tutte polynomial
Year: 2013
OAI identifier: oai:CiteSeerX.psu:
Provided by: CiteSeerX
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