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Maps between higher Bruhat orders and higher Stasheff-Tamari posets

Hugh Thomas
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Abstract

We make explict a description in terms of convex geometry of the higher Bruhat orders B(n,d) sketched by Kapranov and Voevodsky. We give an analogous description of the higher Stasheff-Tamari poset S_1(n,d). We show that the map f sketched by Kapranov and Voevodsky from B(n,d) to S([0,n+1],d+1) coincides with the map constructed by Rambau, and is a surjection for d<=2. We construct a map analogous to f from S_1(n,d) to B(n-1,d), and show that it is always a poset embedding. We also give an explicit criterion to determine if an element of B(n-1,d) is in the image of this map.

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Hugh Thomas. 2002-12-07. Maps between higher Bruhat orders and higher Stasheff-Tamari posets. https://arxiv.org/abs/math/0212097

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