Generalized Stirling and Lah numbers
Copyright policy )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.
- University of Tennessee at Knoxville United States
- THE UNIVERSITY OF TENNESSEE United States
Modular lattices, Desarguesian lattices, Exact enumeration problems, generating functions, Bell and Stirling numbers, Bell numbers, Stirling numbers, Theoretical Computer Science, Lah numbers, Binomial coefficients; factorials; \(q\)-identities, \(q\)-calculus and related topics, modular binomial lattices, Discrete Mathematics and Combinatorics
Modular lattices, Desarguesian lattices, Exact enumeration problems, generating functions, Bell and Stirling numbers, Bell numbers, Stirling numbers, Theoretical Computer Science, Lah numbers, Binomial coefficients; factorials; \(q\)-identities, \(q\)-calculus and related topics, modular binomial lattices, Discrete Mathematics and Combinatorics
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