论文标题
男子率Lalanne-Kreweras的互动
The birational Lalanne-Kreweras involution
论文作者
论文摘要
Lalanne-kreweras的相关性是对Dyck路径的一组涉及，该路径集合表现出山谷数量和主要指数统计的对称性。我们定义了Lalanne-Kreweras的分段线性和异性扩展。实际上，我们表明Lalanne-Kreweras的互动是一个名为RowVacuation的更普通操作员的特殊情况，该案例作用于任何分级Poset的抗小节。像密切相关和研究的行动式操作员一样，划分量是切换的组成。我们通过使用爱因斯坦和propp的分段线性和birational旋转的方式来获得Lalanne-kreweras互动的分段线性和异性升降。我们表明，Lalanne-Kreweras的相互作用的对称性扩展到了这些分段线性和异性升降机。
The Lalanne-Kreweras involution is an involution on the set of Dyck paths which combinatorially exhibits the symmetry of the number of valleys and major index statistics. We define piecewise-linear and birational extensions of the Lalanne-Kreweras involution. Actually, we show that the Lalanne-Kreweras involution is a special case of a more general operator, called rowvacuation, which acts on the antichains of any graded poset. Rowvacuation, like the closely related and more studied rowmotion operator, is a composition of toggles. We obtain the piecewise-linear and birational lifts of the Lalanne-Kreweras involution by using the piecewise-linear and birational toggles of Einstein and Propp. We show that the symmetry properties of the Lalanne-Kreweras involution extend to these piecewise-linear and birational lifts.
