Christian Stump
Published 2014-04-07, updated 2014-05-23Version 2
In this note, we provide a bijection between a new collection of words on nonnegative integers of length n and Dyck paths of length 2n-2, thus proving that this collection belongs to the Catalan family. The surprising key step in this bijection is the zeta map which is an important map in the study of q,t-Catalan numbers. Finally we discuss an alternative approach to this new collection of words using two statistics on planted trees that turn out to be closely related to the Tutte polynomial on the Catalan matroid.
Comments: 5 pages, v2: title changed + fixed typos; final version
Journal: Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.1
Chain decompositions of q,t-Catalan numbers III: tail extensions and flagpole partitions
Fourientation activities and the Tutte polynomial
Generalized Bijective Maps between $G$-Parking Functions, Spanning Trees, and the Tutte Polynomial
![QR code for arXiv:1404.1708 [math.CO]](http://oss.arxitics.com/images/favicon.svg)