English

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

Combinatorics 2007-05-23 v1

Abstract

Up-down permutations are counted by tangent resp. 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 a la Andrews/Foata/Gessel are also discussed.

Keywords

Cite

@article{arxiv.math/9910096,
  title  = {Combinatorics of geometrically distributed random variables: New q-tangent and q-secant numbers},
  author = {Helmut Prodinger},
  journal= {arXiv preprint arXiv:math/9910096},
  year   = {2007}
}

Comments

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