AbstractWe consider the t-core of an s-core partition, when s and t are coprime positive integers. Olsson has shown that the t-core of an s-core is again an s-core, and we examine certain actions of the affine symmetric group on s-cores which preserve the t-core of an s-core. Along the way, we give a new proof of Olssonʼs result. We also give a new proof of a result of Vandehey, showing that there is a simultaneous s- and t-core which contains all others
Let p and q be distinct primes, n an integer with n> p2q2. Then there is no partition of n which ...
AbstractFor a positive integer t, a partition is said to be a t-core if each of the hook numbers fro...
AbstractTextLet s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane a...
AbstractIf s and t are relatively prime positive integers we show that the s-core of a t-core partit...
$t$-core partitions have played important roles in the theory of partitions and related areas. In t...
AbstractIn this paper, the authors investigate the question of when a partition of n∈N is an s-core ...
Abstract. In this paper, the authors investigate the question of when a partition of n ∈ N is an s-c...
AbstractIf s and t are relatively prime positive integers we show that the s-core of a t-core partit...
Let $\ell,k$ be fixed positive integers. In an earlier work, the first and third authors es...
AbstractWe prove that if t is an integer with t=8 or t⩾10, then every integer n>2 has a self-conjuga...
A partition of a positive integer n is a nonincreasing sequence of positive integers with sum $n.$ H...
We prove a refinement of the t-core conjecture proven by Granville and Ono. We show that for every n...
In this paper, the authors investigate the question of when a partition of n∈N is an s-core and also...
AbstractA conjecture on the monotonicity of t-core partitions in an article of Stanton [Dennis Stant...
AbstractTextLet s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane a...
Let p and q be distinct primes, n an integer with n> p2q2. Then there is no partition of n which ...
AbstractFor a positive integer t, a partition is said to be a t-core if each of the hook numbers fro...
AbstractTextLet s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane a...
AbstractIf s and t are relatively prime positive integers we show that the s-core of a t-core partit...
$t$-core partitions have played important roles in the theory of partitions and related areas. In t...
AbstractIn this paper, the authors investigate the question of when a partition of n∈N is an s-core ...
Abstract. In this paper, the authors investigate the question of when a partition of n ∈ N is an s-c...
AbstractIf s and t are relatively prime positive integers we show that the s-core of a t-core partit...
Let $\ell,k$ be fixed positive integers. In an earlier work, the first and third authors es...
AbstractWe prove that if t is an integer with t=8 or t⩾10, then every integer n>2 has a self-conjuga...
A partition of a positive integer n is a nonincreasing sequence of positive integers with sum $n.$ H...
We prove a refinement of the t-core conjecture proven by Granville and Ono. We show that for every n...
In this paper, the authors investigate the question of when a partition of n∈N is an s-core and also...
AbstractA conjecture on the monotonicity of t-core partitions in an article of Stanton [Dennis Stant...
AbstractTextLet s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane a...
Let p and q be distinct primes, n an integer with n> p2q2. Then there is no partition of n which ...
AbstractFor a positive integer t, a partition is said to be a t-core if each of the hook numbers fro...
AbstractTextLet s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane a...
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