Bijective link between Chapoton's new intervals and bipartite planar maps
Combinatorics
2021-06-18 v2
Abstract
In 2006, Chapoton defined a class of Tamari intervals called "new intervals" in his enumeration of Tamari intervals, and he found that these new intervals are equi-enumerated with bipartite planar maps. We present here a direct bijection between these two classes of objects using a new object called "degree tree". Our bijection also gives an intuitive proof of an unpublished equi-distribution result of some statistics on new intervals given by Chapoton and Fusy.
Keywords
Cite
@article{arxiv.2001.04723,
title = {Bijective link between Chapoton's new intervals and bipartite planar maps},
author = {Wenjie Fang},
journal= {arXiv preprint arXiv:2001.04723},
year = {2021}
}
Comments
19 pages, 7 figures, extended abstract submitted to FPSAC 2020. To appear on European J. Combin. 97 (2021)