Counting self-conjugate (s,s+1,s+2)-core partitions

Hyunsoo Cho, JiSun Huh, Jaebum Sohn

We are concerned with counting self-conjugate $(s,s+1,s+2)$-core partitions. A Motzkin path of length $n$ is a path from $(0,0)$ to $(n,0)$ which stays above the $x$-axis and consi…