Séminaire Lotharingien de Combinatoire, 84B.11 (2020), 12 pp.
Wenjie Fang
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 equinumerous 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intuitive proof of an unpublished equi-distribution result of some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.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
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