论文标题
321避开排列的行动
Rowmotion on 321-avoiding permutations
论文作者
论文摘要
我们通过涉及Dyck路径和Lalanne-Kreweras互动的双线翻译，以321美元的避免排列给出了RowMotion的自然定义，这是$ A类型$ a $的抗小节的类似概念。我们证明，某些置换统计（例如固定点的数量）在RowMotion下是同质的，这意味着它们在其轨道上具有恒定的平均值。 Our setting also provides a more natural description of the celebrated Armstrong--Stump--Thomas equivariant bijection between antichains and non-crossing matchings in types $A$ and $B$, by showing that it is equivalent to the Robinson--Schensted--Knuth correspondence on $321$-avoiding permutations permutations.
We give a natural definition of rowmotion for $321$-avoiding permutations, by translating, through bijections involving Dyck paths and the Lalanne--Kreweras involution, the analogous notion for antichains of the positive root poset of type $A$. We prove that some permutation statistics, such as the number of fixed points, are homomesic under rowmotion, meaning that they have a constant average over its orbits. Our setting also provides a more natural description of the celebrated Armstrong--Stump--Thomas equivariant bijection between antichains and non-crossing matchings in types $A$ and $B$, by showing that it is equivalent to the Robinson--Schensted--Knuth correspondence on $321$-avoiding permutations permutations.
