Shi-Mei Ma, Jun Ma, Yeong-Nan Yeh
Published 2018-05-28Version 1
The Legendre-Stirling numbers of the second kind were introduced by Everitt et al. in the spectral theory of powers of the Legendre differential expressions. In this paper, we provide a combinatorial code for Legendre-Stirling set partitions. As an application, we obtain combinatorial expansions of the Legendre-Stirling numbers of both kinds. Moreover, we present grammatical descriptions of the Jacobi-Stirling numbers of both kinds.
Stirling numbers for complex reflection groups
Eulerian polynomials, perfect matchings and Stirling permutations of the second kind
A $q,r$-analogue of poly-Stirling numbers of second kind with combinatorial applications
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