Counting isomorphism classes of $\beta$-normal linear lambda terms

Noam Zeilberger (1)

1 MSR - INRIA - Microsoft Research - Inria Joint Centre

Unanticipated connections between different fragments of lambda calculus and different families of embedded graphs (a.k.a. "maps") motivate the problem of enumerating $\beta$-normal linear lambda terms. In this brief note, it is shown (by appeal to a theorem of Arqu\`es and Beraud) that the sequence counting isomorphism classes of $\beta$-normal linear lambda terms up to free exchange of adjacent lambda abstractions coincides with the sequence counting isomorphism classes of rooted maps on oriented surfaces (A000698).

Domaines: Logique en informatique [cs.LO]; Combinatoire [math.CO]

Noam Zeilberger. Counting isomorphism classes of $\beta$-normal linear lambda terms. 2015. ⟨hal-01214121⟩