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Interval decomposition lattices are balanced

Research output: Contribution to journalArticleScientificpeer-review


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


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


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

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Field of science, Statistics Finland

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