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Combinatorics of geometrically distributed random variables: new q -tangent and q -secant numbers

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  • Helmut Prodinger

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 new q -tangent and q -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.

Suggested Citation

  • Helmut Prodinger, 2000. "Combinatorics of geometrically distributed random variables: new q -tangent and q -secant numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-14, January.
    • Handle: RePEc:hin:jijmms:236428
    DOI: 10.1155/S0161171200004439
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