Sweep maps are a family of maps on words that, while simple to define, are not yet known to be injective in general. This family subsumes many of the "zeta maps" that have arisen in the study of q,t-Catalan numbers in the course of relating the three statistics of area, bounce and dinv. A sweep map can be defined for words over arbitrary alphabets with arbitrary weights. The latter property makes them particularly suitable for the study of rational Catalan combinatorics.

Source : oai:HAL:hal-01207541v1

Volume: DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)

Section: Proceedings

Published on: January 1, 2014

Submitted on: November 21, 2016

Keywords: q,t-Catalan numbers,Dyck paths,zeta map,diagonal harmonics,nabla operator,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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