Minimal paths between maximal chains in finite rank semimodular lattices
type: Item
instance of: scholarly article
title: Minimal paths between maximal chains in finite rank semimodular lattices
zbMATH Open document ID: 0903.06006
DOI: 10.1023/A:1008615111070
author: David S. Herscovici
published in: Journal of Algebraic Combinatorics
publication date: 1998-04-13T00:00:00Z
review text: The author studies relationships between maximal chains (``flags'') in a finite rank semimodular lattice, namely, the union of all flags on at least one minimum length path connecting two flags. He generalizes to semimodular lattices the Jordan-Hölder permutation and results concerning the sublattice generated by two flags. He relates minimal paths between two flags in a semimodular lattice to reduced decompositions of the Jordan-Hölder permutation between the flags. Many results of the paper use a comparison of the subposet of all points on at least one reduced \(X\)-\(Y\) path to the sublattice generated by two flags \(X\) and \(Y\) in a semimodular lattice and labeling functions with respect to flags. Finally, the author classifies the sets of reduced decompositions of a permutation which can correspond to a set of reduced \(X\)-\(Y\) paths in some semimodular lattice.
Mathematics Subject Classification ID: 06C10
zbMATH DE Number: 1139615
zbMATH Keywords: minimal paths between flags
zbMATH Keywords: maximal chains
zbMATH Keywords: finite rank semimodular lattice
zbMATH Keywords: reduced decompositions
zbMATH Keywords: Jordan-Hölder permutation
reviewed by: Bohumil František Šmarda
MaRDI profile type: Publication
cites work: The gallery distance of flags
cites work: The geometry of the chamber system of a semimodular lattice
cites work: Q5331549
cites work: Shellable and Cohen-Macaulay Partially Ordered Sets
cites work: Q5619114
cites work: Q3956998
cites work: Q4165427
cites work: Semimodular lattices and semibuildings
cites work: Q4692803
cites work: Q3748279
cites work: Supersolvable lattices
cites work: Finite lattices and Jordan-Hölder sets
description: scientific article; zbMATH DE number 1139615