In 2007, Olsson and Stanton determined the largest size of $(t_1,t_2)$-core partitions. Inspired by their result, there have been considerable research on the largest size of simultaneous core partitions. In this work, we compute the largest size of $(t,t+d,t+2d)$-core partitions for any coprime positive integers $t$ and $d$. This generalizes the result by Yang, Zhong, and Zhou, who proved the largest size of $(t,t+1,t+2)$-core partitions.
@article{10_37236_13696,
author = {Hyunsoo Cho and Kyeongjun Lee and Hayan Nam},
title = {The largest size of \((t, t+d, t+2d)\)-core partitions},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {2},
doi = {10.37236/13696},
zbl = {1569.05022},
url = {http://geodesic.mathdoc.fr/articles/10.37236/13696/}
}
TY - JOUR
AU - Hyunsoo Cho
AU - Kyeongjun Lee
AU - Hayan Nam
TI - The largest size of \((t, t+d, t+2d)\)-core partitions
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/13696/
DO - 10.37236/13696
ID - 10_37236_13696
ER -
%0 Journal Article
%A Hyunsoo Cho
%A Kyeongjun Lee
%A Hayan Nam
%T The largest size of \((t, t+d, t+2d)\)-core partitions
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/13696/
%R 10.37236/13696
%F 10_37236_13696
Hyunsoo Cho; Kyeongjun Lee; Hayan Nam. The largest size of \((t, t+d, t+2d)\)-core partitions. The electronic journal of combinatorics, Tome 32 (2025) no. 2. doi: 10.37236/13696
