On the distribution of rank and crank statistics for integer partitions View Full Text


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Article Info

DATE

2019-06

AUTHORS

Nian Hong Zhou

ABSTRACT

Let k be a positive integer and m be an integer. Garvan’s k-rank Nk(n,m) is the number of partitions of n into at least (k-1) successive Durfee squares with k-rank equal to m. In this paper we give some asymptotics for Nk(n,m) with |m|≥n as n→∞. As a corollary, we give a more complete answer for the Dyson’s crank distribution conjecture. We also establish some asymptotic formulas for finite differences of Nk(n,m) with respect to m with m≫nlogn. More... »

PAGES

18

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http://scigraph.springernature.com/pub.10.1007/s40993-019-0156-z

DOI

http://dx.doi.org/10.1007/s40993-019-0156-z

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https://app.dimensions.ai/details/publication/pub.1112857276


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