ar X iv : 0 90 5 . 28 99 v 2 [ m at h . C O ] 2 0 M ay 2 00 9 COMBINATORIAL INTERPRETATIONS OF THE JACOBI - STIRLING NUMBERS
نویسنده
چکیده
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.
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