Journée "Cartes Aléatoires"

Bijective Link Between Chapoton's New Intervals and Bipartite Planar Maps

by Wenjie Fang (LIGM)

Centre de conférences Marilyn et James Simons (I.H.E.S.)

Centre de conférences Marilyn et James Simons


Le Bois-Marie 35, route de Chartres 91440 Bures-sur-Yvette

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 Our bijection also gives an intuitive proof of an unpublished equi-distribution result of some statistics on new intervals given by Chapoton and Fusy.

Organized by

Guillaume Blanc (LMO) & Alice Contat (LMO)