Enumeration in the lattice of q-decreasing words
Jean-Luc Baril, Nathanaël Hassler, Sergey Kirgizov
我们证明,配备组件顺序的q-减少词的poset形成了一个格子。 我们列举了任意 q>0, 的连接不可还原元素,对于任何正等数 q, 我们确定覆盖物的数量、间隔和可满足不可还原的元素。 后者在2⌈q⌉+1字母的字母表上呈现与单词相同的结构,避免⌈q⌉^2+2⌈q⌉-1连续模式长度2。 此外,我们分析了其中几个量的渐近行为。
We prove that the poset of q-decreasing words equipped with the componentwise order forms a lattice. We enumerate the join-irreducible elements for arbitrary q>0, and for any positive rational number q, we determine the number of coverings, intervals and meet-irreducible elements. The latter present the same structure as words over an alphabet of 2⌈ q⌉+1 letters avoiding ⌈ q⌉^2+2⌈ q⌉-1 consecutive patterns of length 2. Furthermore, we analyze the asymptotic behavior of several of these quantitie...