Maps between higher Bruhat orders and higher Stasheff-Tamari posets

2002/12/06 by Hugh Thomas, Thomas, Hugh
Mathematics · #06A07 #52B05 (Primary) #52B12 #57Q15 (Secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #math.CO #math.MG #msc:06A07 #msc:52B05 #msc:52B12 #msc:57Q15

paper · pdf · doi:10.48550/arxiv.math/0212097

26 pages, 5 figures. Changes from version one are minor and confined to one paragraph

openalex publication_date 2002/12/06 · arxiv created 2002/12/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S₁(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 S₁(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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