论文标题
塔玛里和戴克晶格的线性间隔以及alt-tamari posets中的线性间隔
Linear Intervals in the Tamari and the Dyck Lattices and in the alt-Tamari Posets
论文作者
论文摘要
我们使用生成序列和拉格朗日反转来计算Tamari和Dyck Lattices中线性间隔的数量。令人惊讶的是，这些数字在两个晶格中都是相同的。我们在Dyck Paths上定义了一个新的POSET家族，我们称之为Alt-Tamari Posets。每个alt-tamari poset都取决于{0,1}^n中的增量函数delta的选择。我们将tamari和Dyck晶格恢复为Delta = 1和Delta = 0的极端情况。我们证明，所有的Alt-Tamari Posets具有任何给定高度的线性间隔相同。
We count the number of linear intervals in the Tamari and the Dyck lattices according to their height, using generating series and Lagrange inversion. Surprisingly, these numbers are the same in both lattices. We define a new family of posets on Dyck paths, which we call alt-Tamari posets. Each alt-Tamari poset depends on the choice of an increment function delta in {0,1}^n. We recover the Tamari and the Dyck lattices as extreme cases with delta = 1 and delta = 0, respectively. We prove that all the alt-Tamari posets have the same number of linear intervals of any given height.
