Journal of Integer Sequences, Vol. 7 (2004), Article 04.1.3

Enumeration of Concave Integer Partitions


Jan Snellman and Michael Paulsen
Department of Mathematics
Stockholm University
SE-10691 Stockholm
Sweden

Abstract:

An integer partition \(\lambda \vdash n\) corresponds, via its Ferrers diagram, to an artinian monomial ideal \(I \subset {\mathbb{C} }[x,y]\) with \(\dim_{\mathbb{C} }{\mathbb{C} }[x,y]/I = n\). If \(\lambda\) corresponds to an integrally closed ideal we call it concave . We study generating functions for the number of concave partitions, unrestricted or with at most r parts.


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(Concerned with sequences A007294 A086159 A086160 A008620 A004913 A086161 A086162 A086163 .)

Received October 6 2003; revised version received February 11 2004. Published in Journal of Integer Sequences February 11 2004.

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