2012/07/31 by Luca Ferrari, Ferrari, Luca
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #math.CO #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1207.7295
15 pages. To appear on Journal of Combinatorial Mathematics and Combinatorial Computing
arxiv created 2012/07/31 · openalex publication_date 2012/07/31 · arxiv updated 2012/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an original approach to the problem of rankunimodality for Dyck lattices. It is based on a well known recursive construction of Dyck paths originally developed in the context of the ECO methodology, which provides a partition of Dyck lattices into saturated chains. Even if we are not able to prove that Dyck lattices are rank-unimodal, we describe a family of polynomials (which constitutes a polynomial analog of ballot numbers) and a succession rule which appear to be useful in addressing such a problem. At the end of the paper, we also propose and begin a systematic investigation of the problem of unimodality of succession rules.