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arXiv · 1805.10998

On certain combinatorial expansions of the Legendre-Stirling numbers

Shi-Mei Ma·Jun Ma·Yeong-Nan Yeh
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Abstract

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.

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Shi-Mei Ma, Jun Ma, Yeong-Nan Yeh. 2018-05-28. On certain combinatorial expansions of the Legendre-Stirling numbers. https://arxiv.org/abs/1805.10998

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