论文标题
通过幼小的tableaux进行验证停车功能公式
Toward a Schurification of Parking Function Formulas via bijections with Young Tableaux
论文作者
论文摘要
本文包含\ cite {[H2008]}的开放问题3.11的部分答案。那是为了在Schröder路径上找到一个明确的培训，该路径会颠倒统计区域并反弹。本文最初是作为试图在$ m $-schröder路径上写入总和，并在变量$ q $和$ t $中使用固定数量的对角线步骤。 Some results have been generalized to parking functions, and some bijections were made with standard Young tableaux giving way to partial combinatorial formulas in the basis $s_μ(q,t)s_λ(X)$ for $\nabla(e_n)$ (respectively, $\nabla^m(e_n)$), when $μ$ and $λ$ are hooks (respectively, $μ$ is of length one).我们还提供了一种显式算法，该算法给出了与Schur函数$S_μ（Q，T）$相关的所有Schröder路径，当$μ$长度为一。从某种意义上说，这是Schröder路径分为晶体的部分分解。
This paper contains a partial answer to the open problem 3.11 of \cite{[H2008]}. That is to find an explicit bijection on Schröder paths that inverts the statistics area and bounce. This paper started as an attempt to write the sum over $m$-Schröder paths with a fix number of diagonal steps into Schur functions in the variables $q$ and $t$. Some results have been generalized to parking functions, and some bijections were made with standard Young tableaux giving way to partial combinatorial formulas in the basis $s_μ(q,t)s_λ(X)$ for $\nabla(e_n)$ (respectively, $\nabla^m(e_n)$), when $μ$ and $λ$ are hooks (respectively, $μ$ is of length one). We also give an explicit algorithm that gives all the Schröder paths related to a Schur function $s_μ(q,t)$ when $μ$ is of length one. In a sense, it is a partial decomposition of Schröder paths into crystals.
