University of Minnesota Combinatorics Seminar
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Abstract |
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The associahedron is a polytope whose vertex-edge-graph
is isomorphic to the flip graph of an associated convex polygon
and there are many interesting ways to obtain realisations. I focus
on realisations that are generalised permutahedra obtained by
Hohlweg and Lange. As shown by Ardila, Benedetti and Doker,
generalised permutahedra have a Minkowski decomposition
into faces of a standard simplex and Möbius inversion relates
the right-hand sides of inequalities to the coefficients of this
decomposition.
I will review the construction of Hohlweg and Lange, show that the general formula of Ardila, Benedetti and Doker can be significantly simplified for these instances and give a combinatorial interpretation of the Minkowski coefficients in terms of certain path lengths of the associated polygon.
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