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.
Lattices of lattice paths / Ferrari, Luca; Pinzani, Renzo. - In: JOURNAL OF STATISTICAL PLANNING AND INFERENCE. - ISSN 0378-3758. - STAMPA. - 135:(2005), pp. 77-92.
Lattices of lattice paths
FERRARI, LUCA;PINZANI, RENZO
2005
Abstract
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.
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