Luca Ferrari, Renzo Pinzani
Published 2004-11-19Version 1
We consider posets of lattice paths (endowed with a natural order) and begin the study of such structures. We give an algebraic condition to recognize which ones of these posets are lattices. Next we study the class of Dyck lattices (i.e., lattices of Dyck paths) and give a recursive construction for them. The last section is devoted to the presentation of a couple of open problems.
Comments: 19 pages, presented at the conference "Lattice path combinatorics and discrete distributions", Athens (Greece), 2002. To be published on Journal of Statistical Planning and Inference
Unimodality and Dyck paths
Refinements of Lattice paths with flaws
A bijection between bargraphs and Dyck paths
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