Noncrossing Partitions, Toggles, and Homomesies

[摘要] We introduce $n(n-1)/2$ natural involutions ("toggles") on the set $S$ of noncrossing partitions $\pi$ of size $n$, along with certain composite operations obtained by composing these involutions. We show that for many operations $T$ of this kind, a surpr

[学科分类] 离散数学和组合数学

[关键词] Coxeter element;Homomesy;Involution;Noncrossing partition;Toggle group