Year: 2012
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Ferrari, Luca
Institution: University of Florence
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2474728107