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

Noam Zeilberger

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arXiv · 1509.07596

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

Noam Zeilberger

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Abstract

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).

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Noam Zeilberger. 2015-09-25. Counting isomorphism classes of $\beta$-normal linear lambda terms. https://arxiv.org/abs/1509.07596

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