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Triangulations of cyclic polytopes and higher Bruhat orders
Author(s) -
Rambau Jörg
Publication year - 1997
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/s0025579300012055
Subject(s) - combinatorics , polytope , mathematics , partially ordered set , conjecture , bounded function , lattice (music) , physics , mathematical analysis , acoustics
Recently Edelman and Reiner suggested two poset structures,S 1 ( n , d ) andS 2 ( n , d ) on the set of all triangulations of the cyclic d ‐polytope C ( n , d ) with n vertices. Both posets are generalizations of the well‐studied Tamari lattice. WhileS 2 ( n , d ) is bounded by definition, the same is not obvious forS 1 ( n , d ). In the paper by Edelman and Reiner the bounds ofS 2 ( n , d ) were also confirmed forS 1 ( n , d ) whenever d ≤5, leaving the general case as a conjecture.