The type B permutohedron and the poset of intervals as a Tchebyshev transform

2020/07/14 by Hetyei, Gábor · 1 citation
#05E45 #52B05 #Combinatorics (math.CO) #FOS: Mathematics #Primary 06A07 #Secondary 05A15

paper · doi:10.48550/arxiv.2007.07362

Abstract

We show that the order complex of intervals of a poset, ordered by inclusion, is a Tchebyshev triangulation of the order complex of the original poset. Besides studying the properties of this transformation, we show that the dual of the type B permutohedron is combinatorially equivalent to the suspension of the order complex of the poset of intervals of a Boolean algebra (with the minimum and maximum elements removed).

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• Eulerian posets and Z-polynomials

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