拉链合并连续整数组合的张量中Dyck词的表示
Representation of Dyck words in tensors that zipper merge contiguous integer compositions
摘要：
令$0<k\in\mathbb{Z}$。我们拉链合并整数组合与总和$k$和$k+1$，相等数量的部分和初始条目至少等于1和2，分别。这将产生具有两个初始零、$k-1$剩余零和$k$ 1的位串。其条目是这样的位串的张量包含长度为$2k$的所有Dyck字的唯一表示。如果这些张量的行和列按字典序降序排列，则它们不代表戴克词的条目形成对应于严格下三角子矩阵的下降楼梯的不相交并集。
英文摘要：
Let $0<k\in\mathbb{Z}$. We zipper-merge integer compositions with sums $k$ and $k+1$, equal number of parts and initial entries equal at least to 1 and 2, respectively. This yields bitstrings with two initial zeros, $k-1$ remaining zeros and $k$ ones. Tensors whose entries are such bitstrings contain unique representations of all Dyck words of length $2k$. If rows and columns of such tensors are disposed in descending lexicographic order, then their entries not representing Dyck words form disjoint unions of descending staircases corresponding to strict lower triangular submatrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
