论文标题
在序列的限制上
On the limit of the sequence $\left\{ C^m(D) \right\}_{m=1}^{\infty}$ for a multipartite tournament $D$
论文作者
论文摘要
对于整数$ k \ ge 2 $，让$ a $为布尔块矩阵，带有块$ a_ {ij} $的$ 1 \ le i，j \ le k $，以至于$ a_ {ii} $是零矩阵和$ a_ {ij}+a_ __ {ji}+a_ { $ a_ {ij} $和$ a_ {ji}^t $等于$ 1 $ $ i \ neq j $。 Jung〜 {\ Em等人} [多部分比赛的竞争期。 {\ IT线性和多线性代数}，https://doi.org/10.1080/03087.2022.2038057]研究了矩阵序列$ \ {a^m（a^t）本文是上述论文的自然延伸，是由$ \ {a^m（a^t）^m \} _ {m = 1}^{\ infty} $收敛的观察，如果$ a $ a $没有零行，则计算矩阵序列序列的极限， $ \ {a^m（a^t）^m \} _ {m = 1}^{\ infty} $如果$ a $没有零行。为此，我们采用了图形理论方法：注意$ a $是多部分锦标赛$ d $的邻接矩阵，我们计算图形序列$ \ left \ left \ {c^m（d）\ right \} _ {m = 1}^}^}^{\ infty} $当$ d $ d $ d $ n n n n n n n n sands sinds。
For an integer $k \ge 2$, let $A$ be a Boolean block matrix with blocks $A_{ij}$ for $1 \le i,j \le k$ such that $A_{ii}$ is a zero matrix and $A_{ij}+A_{ji}^T$ is a matrix with all elements $1$ but not both corresponding elements of $A_{ij}$ and $A_{ji}^T$ equal to $1$ for $i \neq j$. Jung~{\em et al.} [Competition periods of multipartite tournaments. {\it Linear and Multilinear Algebra}, https://doi.org/10.1080/03081087.2022.2038057] studied the matrix sequence $\{A^m(A^T)^m\}_{m=1}^{\infty}$. This paper, which is a natural extension of the above paper and was initiated by the observation that $\{A^m(A^T)^m\}_{m=1}^{\infty}$ converges if $A$ has no zero rows, computes the limit of the matrix sequence $\{A^m(A^T)^m\}_{m=1}^{\infty}$ if $A$ has no zero rows. To this end, we take a graph theoretical approach: noting that $A$ is the adjacency matrix of a multipartite tournament $D$, we compute the limit of the graph sequence $\left\{ C^m(D) \right\}_{m=1}^{\infty}$ when $D$ has no sinks.
