Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1078,
author = {Stephan Foldes and S\'andor Radeleczki},
title = {On interval decomposition lattices},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {24},
year = {2004},
pages = {95-114},
zbl = {1062.06011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1078}
}
Stephan Foldes; Sándor Radeleczki. On interval decomposition lattices. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 95-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1078/
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