Combinatorics of geometrically distributed random variables: new q-tangent and q-secant numbers. (15th December 2000)

• Record Type: Journal Article
• Authors: Prodinger, Helmut
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 24:Number 12(2000)
• Page Start: 825
• Page End: 838
• Publication Date: 2000-12-15
• Subjects: Tangent numbers -- secant numbers -- alternating permutations -- geometric distribution -- q-analogues; Mathematics -- Periodicals; 510.5
• DOI: 10.1155/S0161171200004439
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Up-down permutations are counted by tangent (respectively, secant) numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all coincide with the classical version. In this way, we get some newq -tangent andq -secant functions. Some of them also have nice continued fraction expansions; in one particular case, we could not find a proof for it. Divisibility results à la Andrews, Foata, Gessel are also discussed.