publication . Preprint . 2009

Combinatorial interpretations of the Jacobi-Stirling numbers

Gelineau, Yoann; Zeng, Jiang;
Open Access English
  • Published: 18 May 2009
  • Publisher: HAL CCSD
14 pages; The Jacobi-Stirling numbers of the first and second kinds were introduced in 2006 in the spectral theory and are polynomial refinements of the Legendre-Stirling numbers. Andrews and Littlejohn have recently given a combinatorial interpretation for the second kind of the latter numbers. Noticing that these numbers are very similar to the classical central factorial numbers, we give combinatorial interpretations for the Jacobi-Stirling numbers of both kinds, which provide a unified treatment of the combinatorial theories for the two previous sequences and also for the Stirling numbers of both kinds.
arxiv: Computer Science::Symbolic ComputationMathematics::History and OverviewMathematics::Combinatorics
free text keywords: signed partitions, Riordan complexes, Legendre-Stirling numbers, central factorial numbers, Stirling numbers, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], Jacobi-Stirling numbers, 05A05, 05A15, 33C45, 05A10, 05A18, 34B24, quasi-permutations, simply hooked quasi-permutations
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