English

About maximal antichains in a product of two chains:A catch-all note

Combinatorics 2024-10-31 v2

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.

Keywords

Cite

@article{arxiv.2410.16243,
  title  = {About maximal antichains in a product of two chains:A catch-all note},
  author = {Denis Bouyssou and Thierry Marchant and Marc Pirlot},
  journal= {arXiv preprint arXiv:2410.16243},
  year   = {2024}
}

Comments

28 pages, 4 figures, 13 tables. Companion paper: ELECTRE TRI-nB, pseudo-disjunctive: axiomatic and combinatorial results (arXiv:2410.18443)