  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.
