Stirling numbers interpolation using permutations with forbidden subsequences

  • Authors:

  • G. Labelle;P. Leroux;E. Pergola;R. Pinzani

  • Affiliations:

  • LaCIM, Département de Mathématiques, Université du Québec à Montréal, CP 8888, Succ. Centre-Ville, Montréal, Québec, Canada;LaCIM, Département de Mathématiques, Université du Québec à Montréal, CP 8888, Succ. Centre-Ville, Montréal, Québec, Canada;Dipartimento di Sistemi e Informatica, Universitá di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy;Dipartimento di Sistemi e Informatica, Universitá di Firenze, Via Lombroso 6/17, 50134 Firenze, Italy

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2002

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Abstract

We present a family of number sequences which interpolates between the sequences Bn, of Bell numbers, and n!. It is defined in terms of permutations with forbidden patterns or subsequences. The introduction, as a parameter, of the number m of right-to-left minima yields an interpolation between Stirling numbers of the second kind S(n,m) and of the first kind (signless) c(n,m). Moreover, q-counting the restricted permutations by special inversions gives an interpolation between variants of the usual q-analogues of these numbers.