论文标题
Dyck编号，I。后继功能
Dyck Numbers, I. Successor Function
论文作者
论文摘要
Dyck路径是研究最广泛的加泰罗尼亚家庭之一。在本文中，我们正在处理戴克路径的最小编号，以及由此产生的数字，即OEIS序列A036991的术语，我们称之为dyck编号。我们考虑在Dyck数字上的后继函数，即获得封闭公式。特别是，计算了Mersenne数字后继商的公式（因为OEIS A000225是A036991的子集）。我们已经获得了DYCK后继函数，DS功能的相应算法，并且已经编译了Python程序。在论文的末尾，A036991范围的大小与OEIS A001405的术语有关。相应的假设是制定的。
Dyck paths are among the most heavily studied Catalan families. In the paper we are dealing with the minimal numbering of Dyck paths, with the resulting numbers, the terms of the OEIS sequence A036991, which we have called Dyck numbers. We consider the successor function on the Dyck numbers, closed formulas are obtained. In particular, the formula for the successor of the Mersenne number is calculated (since OEIS A000225 is a subset of A036991). We have obtained the corresponding algorithm of the Dyck successor function, DS-function, and a Python program has been compiled. At the end of the paper, the size of the A036991 ranges is associated with the terms of OEIS A001405. The corresponding hypothesis is formulated.
