English

On certain combinatorial expansions of the Legendre-Stirling numbers

Combinatorics 2018-05-29 v1

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.

Keywords

Cite

@article{arxiv.1805.10998,
  title  = {On certain combinatorial expansions of the Legendre-Stirling numbers},
  author = {Shi-Mei Ma and Jun Ma and Yeong-Nan Yeh},
  journal= {arXiv preprint arXiv:1805.10998},
  year   = {2018}
}

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11 pages