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arXiv · 1611.05775

Explicit (Polynomial!) Expressions for the Expectation, Variance and Higher Moments of the Size of a (2n + 1, 2n + 3)-core partition with Distinct Parts

Anthony Zaleski·Doron Zeilberger
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Abstract

Inspired by Armin Straub's conjecture (arXiv:1601.07161) about the number and maximal size of (2n+1, 2n+3)-core partitions with distinct parts, we develop relatively efficient, symbolic-computational algorithms, based on non-linear functional recurrences, to generate the generating functions, according to size, of the set of such partitions. By computing these polynomials for n=1,...21, we are able to rigorously derive explicit expressions for the expectation, variance, and third through seventh moments of the random variable "size of a (2n+1, 2n+3)-core partition with distinct parts." In particular, we find that this random variable is not asymptotically normal as n goes to infinity.

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Anthony Zaleski, Doron Zeilberger. 2016-11-17. Explicit (Polynomial!) Expressions for the Expectation, Variance and Higher Moments of the Size of a (2n + 1, 2n + 3)-core partition with Distinct Parts. https://arxiv.org/abs/1611.05775

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