Journal of Combinatorics

Volume 2 (2011)

Number 2

Lattices of paths: Representation theory and valuations

Pages: 265 – 291

DOI: https://dx.doi.org/10.4310/JOC.2011.v2.n2.a5

Authors

Luca Ferrari (Dipartimento di Sistemi e Informatica, Università di Firenze, Italy)

Emanuele Munarini (Dipartimento di Matematica, Politecnico di Milano, Italy)

Abstract

We study some distributive lattices arising in the combinatorics of lattice paths. In particular, for the Dyck, Motzkin and Schröder lattices we describe the spectrum and we determine explicitly the Euler characteristic in terms of natural parameters of lattice paths.

Keywords

Dyck paths, Dyck lattices, Motzkin paths, Motzkin lattices, Schröder paths, Schröder lattices, Dyck-like lattices, Young lattices, Euler characteristic, finite distributive lattices

2010 Mathematics Subject Classification

Primary 06D05. Secondary 06A07.

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Published 25 October 2011