A beautiful recent conjecture of D. Armstrong predicts the average size of a partition that is simultaneously an s-core and a t-core, where s and t are coprime. Our goal is to prove this conjecture when t = s + 1. These simultaneous (s, s + 1)-core partitions, which are enumerated by Catalan numbers, have average size ((s+1)/3)/2.
SIAM Journal on Discrete Mathematics
The Catalan case of Armstrong's conjecture on simultaneous core partitions Read More: https://epubs.siam.org/doi/10.1137/130950318.
SIAM Journal on Discrete Mathematics,
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