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The higher Stasheff-Tamari posets

Part of: Ordered sets

Published online by Cambridge University Press:  26 February 2010

Paul H. Edelman  and
Victor Reiner
Paul H. Edelman
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
Victor Reiner
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, U.S.A.
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Abstract

This paper studies higher dimensional analogues of the Tamari lattice on triangulations of a convex n-gon, by placing a partial order on the triangulations of a cyclic d-polytope. Our principal results are that in dimension d≤3, these posets are lattices whose intervals have the homotopy type of a sphere or ball, and in dimension d≤5, all triangulations of a cyclic d-polytope are connected by bistellar operations.

MSC classification

Secondary: 06A07: Combinatorics of partially ordered sets
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 127 - 154
Copyright
Copyright © University College London 1996

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