About maximal antichains in a product of two chains:A catch-all note
Denis Bouyssou (1), Thierry Marchant (2), Marc Pirlot (3) ((1) CNRS,, Paris, France, (2) Ghent University, Belgium, (3) University of Mons,, Belgium)
TL;DR
This paper explores the structure of maximal antichains in products of two finite linear orders, establishing correspondences with various combinatorial objects and presenting new results on their enumeration.
Contribution
It introduces novel correspondences between maximal antichains and combinatorial objects, and provides new enumeration results for these antichains.
Findings
Established one-to-one correspondences with combinatorial objects
Gathered known results on the number of maximal antichains
Presented new enumeration results
Abstract
We establish one-to-one correspondences between maximal antichains in products of two finite linear orders and other mathematical objects, such as certain alignments of two strings, walks on a grid, lattice paths, words of two or three letters. Leaning on these correspondences, we gather what is known about the number of maximal antichains in products of two finite linear orders and we establish some new results.
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Taxonomy
TopicsProtein Structure and Dynamics · Advanced Thermodynamics and Statistical Mechanics