2025/11/12 by Jean-Luc Baril, Baril, Jean-Luc, Nathanaël Hassler +3 · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2511.09480
openalex publication_date 2025/11/12 · openalex created_date 2025/11/14 · openalex updated_date 2026/07/28
We prove that the poset of q-decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary q>0, and for any positive rational number q, we determine the number of coverings, intervals and meet-irreducible elements. The latter present the same structure as words over an alphabet of 2\lceil q\rceil+1 letters avoiding \lceil q\rceil2+2\lceil q\rceil-1 consecutive patterns of length 2. Furthermore, we analyze the asymptotic behavior of several of these quantities.