Sweep maps for lattice paths

Nicholas A. Loehr (1, 2) , Gregory S. Warrington (3)

1 Department of Mathematics [Blacksburg]
2 Mathematics Department [UNSA Annapolis]
3 Department of Mathematics & Statistics [Burlington]

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.

Mots clés: q; t-Catalan numbers; Dyck paths; zeta map; diagonal harmonics; nabla operator

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

Nicholas A. Loehr, Gregory S. Warrington. Sweep maps for lattice paths. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.667-678, ⟨10.46298/dmtcs.2432⟩. ⟨hal-01207541⟩