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

par Wenjie Fang (LIGM)

mardi 12 avr. 2022, 15:30 → 16:30 Europe/Paris

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

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 Our bijection also gives an intuitive proof of an unpublished equi-distribution result of some statistics on new intervals given by Chapoton and Fusy.