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Bounds on the number of generalized partitions and some applications

Dukes, W. M. B. (2003) Bounds on the number of generalized partitions and some applications. Australasian Journal of Combinatorics, 28. pp. 257-262. ISSN 1034-4942

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Abstract

We present bounds concerning the number of Hartmanis partitions of a finite set. An application of these inequalities improves the known asymptotic lower bound on the number of linear spaces on n points. We also present an upper bound for a certain class of these partitions which bounds the number of Steiner triple and quadruple systems.