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The higher Stasheff‐Tamari posets
Author(s) -
Edelman Paul H.,
Reiner Victor
Publication year - 1996
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300011633
Subject(s) - mathematics , combinatorics , polytope , lattice (music) , regular polygon , partially ordered set , homotopy , convex polytope , dimension (graph theory) , pure mathematics , convex set , geometry , physics , convex optimization , acoustics
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.