Add to ORKGAbstract. Bringmann and Dousse recently established a conjecture of Dyson dealing with the limiting asymptotics of the Andrews-Garvan crank statistic for integer partitions. A direct “sieving” technique is used to establish this conjecture and establish the range of validity. Unlike the approach of Bringmann and Dousse, the technique readily yields the analogous result for Dyson’s partition rank and all of Garvan’s k-rank statistics
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published arti...
12 pagesRecent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between ...
Recent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between two part...
Higher moments of the partition rank and crank statistics have been studied for their connections to...
Abstract. Higher moments of the partition rank and crank statistics have been studied for their conn...
Let $N_k(m,n)$ denote the number of partitions of $n$ with Garvan $k$-rank $m$. It is well-known tha...
Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any...
AbstractGarvan first defined certain “vector partitions” and assigned to each such partition a “rank...
Abstract. In this paper we prove a longstanding conjecture by Freeman Dyson concerning the limiting ...
Using an extension of Wright’s version of the circle method, we obtain asymptotic formulae for parti...
AbstractWe utilize Dyson' concept of the adjoint of a partition to derive an infinite family of new ...
In 1944, Freeman Dyson conjectured the existence of a “crank” function for partitions that would pro...
In this article the rank of a partition of an integer is a certain integer associated with the parti...
The Dyson rank of an integer partition is the difference between its largest part and the number of ...
Several authors have recently considered the smallest positive part missing from an integer partitio...
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published arti...
12 pagesRecent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between ...
Recent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between two part...
Higher moments of the partition rank and crank statistics have been studied for their connections to...
Abstract. Higher moments of the partition rank and crank statistics have been studied for their conn...
Let $N_k(m,n)$ denote the number of partitions of $n$ with Garvan $k$-rank $m$. It is well-known tha...
Andrews, Garvan and Liang introduced the spt-crank for vector partitions. We conjecture that for any...
AbstractGarvan first defined certain “vector partitions” and assigned to each such partition a “rank...
Abstract. In this paper we prove a longstanding conjecture by Freeman Dyson concerning the limiting ...
Using an extension of Wright’s version of the circle method, we obtain asymptotic formulae for parti...
AbstractWe utilize Dyson' concept of the adjoint of a partition to derive an infinite family of new ...
In 1944, Freeman Dyson conjectured the existence of a “crank” function for partitions that would pro...
In this article the rank of a partition of an integer is a certain integer associated with the parti...
The Dyson rank of an integer partition is the difference between its largest part and the number of ...
Several authors have recently considered the smallest positive part missing from an integer partitio...
This is an author's peer-reviewed final manuscript, as accepted by the publisher. The published arti...
12 pagesRecent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between ...
Recent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between two part...