论文标题
促进Kreweras单词
Promotion of Kreweras words
论文作者
论文摘要
kreweras的单词是由N A，N B和N C组成的单词，其中每个前缀的A具有至少与B的数量一样多，并且至少与C一样多。同等地，kreweras单词是poset $ {\ sf v} \ times [n] $的线性扩展。 Kreweras词是由Kreweras在1965年引入的，Kreweras为其枚举提供了非凡的产品公式。随后，他们成为了四分之一飞机的晶格步行理论的一个基本例子。我们在Kreweras单词的集合中研究Schützenberger的晋升运营商。特别是，我们表明，在kreweras单词上促销的3N应用仅交换了B和C。这样做，我们提供了2009年斯坦利问题的第一个答案，除了海曼在1992年在Haiman分类的四个形状家族以外，要求具有“良好”行为的Posets。我们还以Kureperberg's $ \ Mathfrak的$ \ Mathfrak {sl} _3 $ -web-webrient和port trive trive Nikikov to nike of Kreweras sypects thekreweras songe torge torke。在此描述中，Schützenberger的促销活动对应于网络的旋转。
Kreweras words are words consisting of n A's, n B's, and n C's in which every prefix has at least as many A's as B's and at least as many A's as C's. Equivalently, a Kreweras word is a linear extension of the poset ${\sf V}\times [n]$. Kreweras words were introduced in 1965 by Kreweras, who gave a remarkable product formula for their enumeration. Subsequently they became a fundamental example in the theory of lattice walks in the quarter plane. We study Schützenberger's promotion operator on the set of Kreweras words. In particular, we show that 3n applications of promotion on a Kreweras word merely swaps the B's and C's. Doing so, we provide the first answer to a question of Stanley from 2009, asking for posets with `good' behavior under promotion, other than the four families of shapes classified by Haiman in 1992. We also uncover a strikingly simple description of Kreweras words in terms of Kuperberg's $\mathfrak{sl}_3$-webs, and Postnikov's trip permutation associated with any plabic graph. In this description, Schützenberger's promotion corresponds to rotation of the web.
