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Main Title: Triangulations of Cyclic Polytopes and higher Bruhat Orders
Author(s): Rambau, Jörg
Type: Research Paper
Abstract: Recently Edelman & Reiner} suggested two poset structures S}1(n,d) and S}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. While S}2(n,d) is bounded by definition, the same is not obvious for S}1(n,d). In the paper by Edelman & Reiner} the bounds of S}2(n,d) were also confirmed for S}1(n,d) whenever d \le 5, leaving the general case as a conjecture. In this paper their conjecture is answered in the affirmative for all~d, using several new functorial constructions. Moreover, a structure theorem is presented, stating that the elements of S}1(n,d+1) are in one-to-one correspondence to certain equivalence classes of maximal chains in S}1(n,d). In order to clarify the connection between S}1(n,d) and the higher Bruhat order B}(n-2,d-1) of Manin & Schechtman}, we define an order-preserving map from B}(n-2,d-1) to S}1(n,d), thereby concretizing a result by Kapranov & Voevodsky} in the theory of ordered n-categories.
Subject(s): bruhat order
cyclic polytopes
edelman reiner
several new functorial construction
maximal chain
similar method
structure theorem
well-studied tamari lattice
kapranov voevod-sky
general case
order-preserving map
one-to-one correspondence
manin schechtman
ordered n-categories
certain equivalence class
poset structure
cyclic d-polytope
Issue Date: 1996
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1996, 496
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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