A survey of the higher Stasheff-Tamari orders

The Tamari lattice, thought as a poset on the set of triangulations of a convex polygon with n vertices, generalizes to the higher Stasheff-Tamari orders on the set of triangulations of a cyclic d-dimensional polytope having n vertices. This survey discusses what is known about these orders, and what one would like to know about them.

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Metadaten
Institutes:Mathematik
Author: Jörg Rambau, Victor Reiner
Contributing Corporation:University of Minnesota, USA
Year of Completion:2012
SWD-Keyword:Diskrete Geometrie
Tag:Higher Stasheff-Tamari poset; cyclic polytope; cyclic zonotope; higher Bruhat order; triangulation; zonotopal tiling
Dewey Decimal Classification:510 Mathematik
MSC-Classification:52C22 Tilings in n dimensions [See also 05B45, 51M20]
URN:urn:nbn:de:bvb:703-opus-9694
Source:Erscheint in: Müller-Hoissen, Folkert; Pallo, Jean Marcel; Stasheff, Jim (Eds.). Associahedra, Tamari Lattices and Related Structures, Tamari Memorial Festschrift, Series: Progress in Mathematics, Vol. 299. ISBN 978-3-0348-0404-2. Springer, 2012.
Document Type:Preprint
Language:English
Date of Publication (online):13.03.2012