Title

The Catalan case of Armstrong's conjecture on simultaneous core partitions Read More: https://epubs.siam.org/doi/10.1137/130950318

Authors

Richard Stanley, MIT
Fabrizio Zanello, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

3-31-2015

Abstract

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.

Publisher's Statement

© 2015, Society for Industrial and Applied Mathematics. Publisher’s version of record: https://doi.org/10.1137/130950318

Publication Title

SIAM Journal on Discrete Mathematics

Recommended Citation

Stanley, R., & Zanello, F. (2015). 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, 29(1), 658-666. http://doi.org/10.1137/130950318
Retrieved from: https://digitalcommons.mtu.edu/math-fp/56

Version

Publisher's PDF