On simultaneous (s,s + t,s + 2t,…)-core partitions
Document Type
Article
Publication Date
5-1-2026
Department
Department of Mathematical Sciences
Abstract
We consider simultaneous (s, s +t, s +2t,..., s + pt)-core partitions in the large-p limit, or (when s < t), partitions in which no hook may be of length s (mod t). We study generating functions, containment properties, and congruences when s is not coprime to t. As a boundary case of the general study made by Cho, Huh and Sohn, we provide enumerations when s is coprime to t, and answer positively a conjecture of Fayers on the polynomial behavior of the size of the set of simultaneous (s, s + t, s + 2t,..., s + pt)-core partitions when p grows arbitrarily large. Of particular interest throughout is the comparison to the behavior of simultaneous (s,t)-cores.
Publication Title
Discrete Mathematics
Recommended Citation
Keith, W. J.,
Nath, R.,
&
Sellers, J.
(2026).
On simultaneous (s,s + t,s + 2t,…)-core partitions.
Discrete Mathematics,
349(5).
http://doi.org/10.1016/j.disc.2025.114958
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/2364