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On interval decomposition lattices

100%

Foldes S. , Radeleczki S.

Discussiones Mathematicae - General Algebra and Applications

2004

tom 24

nr 1

95-114

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.

Interval decomposition lattices are balanced

84%

Foldes S. , Radeleczki S.

Demonstratio Mathematica

2016

tom Vol. 49, nr 3

271--281

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.