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Interval decomposition lattices are balanced

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Details

Original languageEnglish
Pages (from-to)271-281
Number of pages11
JournalDEMONSTRATIO MATHEMATICA
Volume49
Issue number3
DOIs
Publication statusPublished - 1 Sep 2016
Publication typeA1 Journal article-refereed

Abstract

Intervals in binary or n-ary relations or other discrete structures generalize the concept of an interval in a linearly ordered set. They are defined abstractly as closed sets of a closure system on a set, satisfying certain axioms. Join-irreducible partitions into intervals are characterized in the lattice of all interval decompositions. This result is used to show that the lattice of interval decompositions is balanced, and the case when this lattice is distributive is also characterised.

ASJC Scopus subject areas

Keywords

  • Balanced lattice, Closure system, Interval decomposition, Join-irreducible element, Semimodular lattice, Strong set

Publication forum classification

Field of science, Statistics Finland