欧拉数与$B_n^l$型多边界奇点
Bernoulli-Euler numbers and multiboundary singularities of type $B_n^l$
摘要：
本文研究了多边界奇点$B_n^l$分歧图连通分支数$K_n^l$的性质。这些数推广了经典的Bernoulli-欧拉数。我们证明了数$K_n^l$上的一个递归关系。众所周知，$K^1_n$是$(n{+}1)$阶欧拉数，这就为计算$K_n^l$提供了一个必要的边界条件.我们还找到了小的固定$l$的生成函数的$K_n^l$和写偏微分方程的一般情况。递归关系导致Bernoulli-欧拉数之间的许多关系。我们在论文的最后一部分展示了它们。
英文摘要：
In this paper we study properties of numbers $K_n^l$ of connected components of bifurcation diagrams for multiboundary singularities $B_n^l$. These numbers generalize classic Bernoulli-Euler numbers. We prove a recurrent relation on the numbers $K_n^l$. As it was known before, $K^1_n$ is $(n{+}1)$-th Bernoulli-Euler number, this gives us a necessary boundary condition to calculate $K_n^l$. We also find the generating functions for $K_n^l$ with small fixed $l$ and write partial differential equations for the general case. The recurrent relations lead to numerous relations between Bernoulli-Euler numbers. We show them in the last section of the paper.
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。
