Séminaire Lotharingien de Combinatoire, 89B.5 (2023), 12 pp.
Wenjie Fang
Bijections between Planar Maps and Planar Linear Normal λ-Terms with Connectivity Condition
Abstract.
The enumeration of linear λ-terms has attracted quite some attention recently, partly due to their link to combinatorial maps. In 2019, Zeilberger and Reed conjectured that 3-connected planar linear normal λ-terms have the same counting formula as bipartite planar maps. In this article, we settle this conjecture by giving a direct bijection. We also explore its enumerative consequences. With a similar approach, we give a new and direct bijection between planar linear normal λ-terms and planar maps, whose restriction to 2-connected λ-terms leads to loopless planar maps.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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