3 research outputs found
Bijections for Entringer families
Andr\'e proved that the number of alternating permutations on is equal to the Euler number . A refinement of Andr\'e's result was
given by Entringer, who proved that counting alternating permutations according
to the first element gives rise to Seidel's triangle for computing
the Euler numbers. In a series of papers, using generating function method and
induction, Poupard gave several further combinatorial interpretations for
both in alternating permutations and increasing trees. Kuznetsov,
Pak, and Postnikov have given more combinatorial interpretations of
in the model of trees. The aim of this paper is to provide bijections between
the different models for as well as some new interpretations. In
particular, we give the first explicit one-to-one correspondence between
Entringer's alternating permutation model and Poupard's increasing tree model.Comment: 19 page