Note on the description of join-distributive lattices by permutations

Kira Adaricheva, Gábor Czédli

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Let L be a join-distributive lattice with length n and width(JiL) ≤ k. There are two ways to describe L by k − 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent lattice theoretical way of the second author. We prove that these two approaches are equivalent. Also, we characterize join-distributive lattices by trajectories.

Original languageEnglish
Pages (from-to)155-162
Number of pages8
JournalAlgebra Universalis
Volume72
Issue number2
DOIs
Publication statusPublished - Oct 1 2014

    Fingerprint

Keywords

  • antimatroid
  • convex geometry
  • diamond-free lattice
  • join-distributive lattice
  • permutation
  • semimodular lattice
  • trajectory

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this