Bijective link between Chapoton's new intervals and bipartite planar maps

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 Our bijection also gives an intuitive proof of an unpublished equi-distribution result of some statistics on new intervals given by Chapoton and Fusy.

19 pages, 7 figures, extended abstract submitted to FPSAC 2020. To appear on European J. Combin. 97 (2021)

References in corpus (2)

• Hopf dreams and diagonal harmonics
• A trinity of duality: non-separable planar maps, $\beta$-(1,0) trees and synchronized intervals

Cited by in corpus (1)

• Bijections between planar maps and planar linear normal $\lambda$-terms with connectivity condition