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Article Dans Une Revue Advances in Applied Mathematics Année : 2023

Bijections between planar maps and planar linear normal λ-terms with connectivity condition

Wenjie Fang

Résumé

The enumeration of linear λ-terms has attracted quite some attention recently, partly due to their link to combinatorial maps. Zeilberger and Giorgetti (2015) gave a recursive bijection between planar linear normal λ-terms and planar maps, which, when restricted to 2-connected λ-terms (i.e., without closed sub-terms), leads to bridgeless planar maps. Inspired by this restriction, Zeilberger and Reed (2019) 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 between these two families. Furthermore, using a similar approach, we give a direct bijection between planar linear normal λ-terms and planar maps, whose restriction to 2-connected λ-terms leads to loopless planar maps. This bijection seems different from that of Zeilberger and Giorgetti, even after taking the map dual. We also explore enumerative consequences of our bijections.

Dates et versions

hal-04072134 , version 1 (17-04-2023)

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Wenjie Fang. Bijections between planar maps and planar linear normal λ-terms with connectivity condition. Advances in Applied Mathematics, 2023, 148, pp.102532. ⟨10.1016/j.aam.2023.102532⟩. ⟨hal-04072134⟩
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