Seidel triangle sequences and Bi-Entringer numbers

Dominique Foata (1) , Guo-Niu Han (2)

1 Institut Lothaire
2 IRMA - Institut de Recherche Mathématique Avancée

This Seidel Triangle Sequence Calculus makes it possible to derive several three-variate generating functions, in particular for the Bi-Entringer numbers, which count the alternating permutations according to their lengths, first and last letters. The paper has been motivated by this surprising observation: the number of alternating permutations, whose last letter has a prescribed value and is greater than its first letter, is equal to the Poupard number.

Mots clés: Entringer numbers; Poupard numbers; Bi-Entringer numbers; tangent numbers; secant numbers

Domaines: Combinatoire [math.CO]

Dominique Foata, Guo-Niu Han. Seidel triangle sequences and Bi-Entringer numbers. European Journal of Combinatorics, 2014, 42, pp.243-260. ⟨10.1016/j.ejc.2014.06.007⟩. ⟨hal-01283934⟩