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 Our bijection also gives an intuitive proof of an unpublished equi-distribution result of some statistics on new intervals given by Chapoton and Fusy.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