Showing papers by "Suresh Govindarajan published in 2013"
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TL;DR: In this article, the authors revisited a formula for the number of plane partitions due to Almkvist using the circle method and provided modifications to his formula along with estimates of the errors, and showed that the improved formula continues to be an asymptotic series.
Abstract: We revisit a formula for the number of plane partitions due to Almkvist Using the circle method, we provide modifications to his formula along with estimates of the errors We show that the improved formula continues to be an asymptotic series Nevertheless, an optimal truncation (ie, superasymptotic) of the formula provides exact numbers of plane partitions for all positive integers n 6400 and numbers with estimated errors for larger values For instance, the formula correctly reproduces 305 of the 316 digits of the numbers of plane partitions of 6999 as predicted by the estimated error We believe that an hyperasymptotic truncation might lead to exact numbers for positive integers up to 50000
6 citations
TL;DR: Using modifications of an algorithm due to Bratley–McKay, a sequence of matrices whose entries are given combinatorial interpretations as the number of particular types of skew Ferrers diagrams are able to compute numbers of partitions of positive integers ⩽26 in any dimension.
6 citations