论文标题
4D Dyck三角及其预测
4D Dyck triangle and its projections
论文作者
论文摘要
经典的Dyck三角形，加泰罗尼亚三角形和加泰罗尼亚卷积矩阵是多维Dyck三角形的平面投影。在Dyck路径中，每个节点由四个相互关联的参数中的两个唯一确定：（i）当前括号的位置，（ii）括号的当前不平衡，（iii）查看的左括号的数量，以及（iv）右括号的左括号。最后两个参数可以分别重新定义为当前加泰罗尼亚数字的索引和加泰罗尼亚数字分解中的汇总索引，以达到正方形之和（dyck squares）。对于4D Dyck三角形，我们考虑六个2D预测（其中一些尚未需求）和四个3D预测。
The classic Dyck triangle, the Catalan triangle, and the Catalan convolution matrix are plane projections of the multidimensional Dyck triangle. In the Dyck path, each node is uniquely determined by two of four interrelated parameters: (i) the position of the current parenthesis, (ii) the current unbalance of the parentheses, (iii) the number of viewed left parentheses, and (iv) the same for right parentheses. The last two parameters can be redefined, respectively, as the index of the current Catalan number and the index of the summand in the decomposition of the Catalan number into the sum of squares (Dyck squares). For the 4D Dyck triangle, we consider six 2D projections (some of them are not yet in demand) and four 3D projections.
