Geodesic
Combinatorial interpretations of the Jacobi-Stirling numbers
The electronic journal of combinatorics, Tome 17 (2010)
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The Jacobi-Stirling numbers of the first and second kinds were introduced 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.
DOI : 10.37236/342
Classification : 05A05, 05A15, 33C45, 05A10, 05A18, 34B24 
@article{10_37236_342,
     author = {Yoann Gelineau and Jiang Zeng},
     title = {Combinatorial interpretations of the {Jacobi-Stirling} numbers},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/342},
     zbl = {1228.05012},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/342/}
}
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%A Jiang Zeng
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Yoann Gelineau; Jiang Zeng. Combinatorial interpretations of the Jacobi-Stirling numbers. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/342

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