论文标题
$ 1 $ - 标题的发病率矩阵的表示形式的理论计算：$ 2 $ -Subsets vs. $ n $ -subsets
A representation-theoretic computation of the rank of $1$-intersection incidence matrices: $2$-subsets vs. $n$-subsets
论文作者
论文摘要
令$ w_ {k，n}^{i}（m）$表示矩阵，该矩阵分别由$ k $ -subsets和$ n $ subsets索引，分别为$ m $ element set。行$ s $，列$ t $ of $ w_ {k，n}^{i}（m）$是$ 1 $，如果$ | s \ cap t | = i $，否则为$ 0 $。我们通过使用对称组的表示理论来计算任何字段上矩阵$ w_ {2，n}^{1}（m）$的等级。我们还提供了一个简单的条件，在该条件下，$ w_ {k，n}^{i}（m）$具有大$ p $ -rank。
Let $W_{k,n}^{i}(m)$ denote a matrix with rows and columns indexed by the $k$-subsets and $n$-subsets, respectively, of an $m$-element set. The row $S$, column $T$ entry of $W_{k,n}^{i}(m)$ is $1$ if $|S \cap T| = i$, and is $0$ otherwise. We compute the rank of the matrix $W_{2,n}^{1}(m)$ over any field by making use of the representation theory of the symmetric group. We also give a simple condition under which $W_{k,n}^{i}(m)$ has large $p$-rank.
