论文标题
拆分子空间和TouchArd-Riordan公式的有限田间解释
Splitting subspaces and a finite field interpretation of the Touchard-Riordan Formula
论文作者
论文摘要
我们列举了有限字段上$ 200万美元的$ t $ m $的$ t $ smplitting子空间$ m $ $ m $的数量。当$ t $是常规的分式半完整时，与枚举的替代方法进行比较会导致Touchard-Riordan公式的新证明，用于通过其交叉数来枚举和弦图。
We enumerate the number of $T$-splitting subspaces of dimension $m$ for an arbitrary operator $T$ on a $2m$-dimensional vector space over a finite field. When $T$ is regular split semisimple, comparison with an alternate method of enumeration leads to a new proof of the Touchard-Riordan formula for enumerating chord diagrams by their number of crossings.
