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Workshop

Polynomial invariant and reciprocity theorem for the Hopf monoid of hypergraphs

  • Théo Karaboghossian (Université de Bordeaux, Labri, Paris, France)
E1 05 (Leibniz-Saal)

Abstract

Hop monoids were introduced by Aguiar and Mahajan and use algebra to formalise the notions of merging and spliting of combinatorial objects (words concatenation, graph restriction etc). Aguiar and Ardila have shown a useful application of this formalism in defining and computing polynomial invariants. In this talk I present the notion of Hopf monoid and use the works of Aguiar and Ardila to define a new polynomial invariant on hypergraphs. I then show that this invariant is subject to a reciprocity theorem similar to Stanley’s reciprocity theorem on the chromatic polynomial of a graph. Finally I show how similar results on other combinatorial objects can be found as a consequence of this theorem.

Links

Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Tim Seynnaeve

Max Planck Institute for Mathematics in the Sciences, Leipzig

Rodica Dinu

University of Bucharest

Giulia Codenotti

Freie Universität Berlin

Frank Röttger

Otto-von-Guericke-Universität, Magdeburg