论文标题
$ \ Mathcal {a}（n，k）$上的Bruhat订单和次级Bruhat订单的巧合
The coincidence of the Bruhat order and the secondary Bruhat order on $\mathcal{A}(n,k)$
论文作者
论文摘要
给定带有$ k \ leq n $的非负整数$ n $和一个非负整数$ k $，我们用$ \ mathcal {a}（n，n，k）$表示所有$ n $ n $ n $ -by-n $ n $ $（0,1）$的类，均与恒定行和列$ k $。在本文中，我们表明，当$ \ Mathcal {a}（n，k）$上的Bruhat订单和次级Bruhat订单重合，并且仅当$ 0 \ leq N \ leq N \ leq 5 $或$ k \ in \ in \ in \ in \ {0,1,1,2，n-2，n-2，n-1，n-1，n \} $ with $ N \ n \ geq 6 $ n \ geq 6 $。
Given a positive integer $n$ and a nonnegative integer $k$ with $k\leq n$, we denote by $\mathcal{A}(n,k)$ the class of all $n$-by-$n$ $(0,1)$-matrices with constant row and column sums $k$. In this paper, we show that the Bruhat order and the secondary Bruhat order coincide on $\mathcal{A}(n,k)$ if and only if either $0\leq n\leq 5$ or $k\in\{0,1,2,n-2,n-1,n\}$ with $n\geq 6$.
