论文标题
解决BCC 2022问题的解决方案
Solution to a BCC 2022 problem
论文作者
论文摘要
对于正整数$ n $和$ k $，以使$ k $最多是$ n $，我们在以下两组之间找到明确的一对一对应关系：由$ k $ r $ r $ s，$ k $ $ u $ s，$ n-k $ u $ s和$ n-k $ $ d $ s组成的单词集，其中的第一个字母不是$ d $ $ d $;以及一组长度为2n $的周期的子图$ h $（该周期的标记为顶点不同），因此$ h $具有$ n $ edges和$ k $连接的组件。这解决了2022年7月在兰开斯特大学举行的第29届英国联合会议的托马斯·塞利格（Thomas Selig）的问题。
For positive integers $n$ and $k$ such that $k$ is at most $n$, we find an explicit one-to-one correspondence between the following two sets: the set of words consisting of $k$ $R$s, $k$ $U$s, and $n - k$ $D$s, where the first letter of the word is not $D$; and the set of subgraphs $H$ of a cycle of length $2n$ (where that cycle has differently labelled vertices) such that $H$ has $n$ edges and $k$ connected components. This solves a problem of Thomas Selig from the 29th British Combinatorial Conference held at Lancaster University in July 2022.
