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Main Title: Interval Reductions and Extensions of Orders: Bijections to Chains in Lattices
Author(s): Felsner, Stefan
Gustedt, Jens
Morvan, Michel
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15816
http://dx.doi.org/10.14279/depositonce-14589
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: We discuss bijections that relate families of chains in lattices associated to an order P and families of interval orders defined on the ground set of P. Two bijections of this type have been known:par (1) The bijection between maximal chains in the antichain lattice AA(P) and the linear extensions of P. (2) A bijection between maximal chains in the lattice of maximal antichains AAM(P) and minimal interval extensions of P. par We discuss two approaches to associate interval orders to chains in AA(P). This leads to new bijections generalizing Bijections~1 and~2. As a consequence we characterize the chains corresponding to weak-order extensions and minimal weak-order extensions of P. par Seeking for a way of representing interval reductions of P by chains we came up with the separation lattice S(P). Chains in this lattice encode an interesting subclass of interval reductions of P. Let SM(P) be the lattice of maximal separations in the separation lattice. Restricted to maximal separations the above bijection specializes to a bijection which nicely complements 1 and 2.par (3) A bijection between maximal chains in the lattice of maximal separations SM(P) and minimal interval reductions of P.
Subject(s): interval reduction
chains
lattices
bijections
order P
Issue Date: 1998
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 1998, 590
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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