Generalized Stirling and Lah numbers
The author develops three generalizations of Stirling numbers of the second kind, \(S(n,k)\), and of Lah numbers, within the theory of modular binomial lattices [\textit{P. Doubilet}, \textit{G.-C. Rota} and \textit{R. Stanley}, Proc. 6th Berkeley Sympos. Math. Statist. Probab., Univ. Calif. 1970, 2, 267-318 (1972; Zbl 0267.05002)] which enables the simultaneous combinatorial analysis of finite sets, vector spaces, and chains. These generalizations include in particular the Bender-Goldman and Carlitz-Milne \(q\)-analogues of \(S(n,k)\) for finite vector spaces [see, e.g., \textit{S. C. Milne}, Adv. Math. 43, 173-196 (1982; Zbl 0482.05012)], as well as Ward, Comtet, and Bell numbers with corresponding interpretations.
scientific article; zbMATH DE number 955155