由少数单调多角形覆盖矩形
Covering rectangles by few monotonous polyominoes
摘要：
一个单调的多角形由一个固定的单调连续函数$f:[a,b] \to \mathbb{R}$与$f(k) \notin \mathbb{Z}$的图所满足的所有格单位正方形构成，当$k \in \mathbb{Z}$。我们的主要结果是：格$(m \times n)$ -矩形的单调多项式覆盖的最小基数是$\left\lceil \frac{2}{3}\left(m+n-\sqrt{m^2+n^2-mn}\right)\right\rceil$。本文是由棋盘上直线的排列问题所引起的。
英文摘要：
A monotonous polyomino is formed by all lattice unit squares met by the graph of some fixed monotonous continuous function $f:[a,b] \to \mathbb{R}$ with $f(k) \notin \mathbb{Z}$ whenever $k \in \mathbb{Z}$. Our main result says that the least cardinality of a covering of a lattice $(m \times n)$-rectangle by monotonous polyominoes is $\left\lceil \frac{2}{3}\left(m+n-\sqrt{m^2+n^2-mn}\right)\right\rceil$. The paper is motivated by a problem on arrangements of straight lines on chessboards.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
