Simultaneous Core Partitions: Parameterizations and Sums

Electronic Journal Of Combinatorics

Victor Y. Wang¹ 

关键词: Core partition;    Hook length;    Beta-set;    Group action;    Cyclic shift;    Dyck path;    Rational Catalan number;    Motzkin number;    Numerical semigroup;   

DOI  :  

学科分类：离散数学和组合数学

来源: Electronic Journal Of Combinatorics

【 摘 要 】

Fix coprime $s,t\ge1$. We re-prove, without Ehrhart reciprocity, a conjecture of Armstrong (recently verified by Johnson) that the finitely many simultaneous $(s,t)$-cores have average size $\frac{1}{24}(s-1)(t-1)(s+t+1)$, and that the subset of self-conj

【 授权许可】

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