Abstract. A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simultaneously an s- and a t-core, where s and t are coprime. Our goal in this note is to prove this conjecture when t = s + 1. These cores, which are enumerated by Catalan numbers, have average size s+
Abstract. A partition of a positive integer n is a nonincreasing sequence of positive integers whose...
A partition is an $a$-core partition if none of its hook lengths are divisible by $a$. It is well kn...
A partition is an $a$-core partition if none of its hook lengths are divisible by $a$. It is well kn...
A beautiful recent conjecture of Armstrong predicts the average size of a partition that is simultan...
A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simul...
A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simul...
A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simul...
Fix coprime s; t > 1. We re-prove, without Ehrhart reciprocity, a conjecture of Armstrong (recently ...
8 pagesInternational audienceSimultaneous core partitions have attracted much attention since Anders...
9 pagesInternational audienceMotivated by Amdeberhan's conjecture on $(t,t+1)$-core partitions with ...
We apply lattice point techniques to the study of simultaneous core partitions.Our central observati...
AbstractTextLet s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane a...
Simultaneous core partitions are important objects in algebraic combinatorics. Recently there has be...
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...
Abstract. A partition of a positive integer n is a nonincreasing sequence of positive integers whose...
A partition is an $a$-core partition if none of its hook lengths are divisible by $a$. It is well kn...
A partition is an $a$-core partition if none of its hook lengths are divisible by $a$. It is well kn...
A beautiful recent conjecture of Armstrong predicts the average size of a partition that is simultan...
A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simul...
A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simul...
A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simul...
Fix coprime s; t > 1. We re-prove, without Ehrhart reciprocity, a conjecture of Armstrong (recently ...
8 pagesInternational audienceSimultaneous core partitions have attracted much attention since Anders...
9 pagesInternational audienceMotivated by Amdeberhan's conjecture on $(t,t+1)$-core partitions with ...
We apply lattice point techniques to the study of simultaneous core partitions.Our central observati...
AbstractTextLet s,t be relatively prime positive integers. We prove a conjecture of Aukerman, Kane a...
Simultaneous core partitions are important objects in algebraic combinatorics. Recently there has be...
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...
Abstract. A partition of a positive integer n is a nonincreasing sequence of positive integers whose...
A partition is an $a$-core partition if none of its hook lengths are divisible by $a$. It is well kn...
A partition is an $a$-core partition if none of its hook lengths are divisible by $a$. It is well kn...
Add to ORKG