论文标题
覆盖矩形由几个单调的多元群落覆盖
Covering rectangles by few monotonous polyominoes
论文作者
论文摘要
所有固定单调的连续函数$ f的图形符合的所有晶格单位正方形均形成单调多元，$ f：[a，b] \ to \ mathbb {r} $带有$ f（k）\ notin \ notin \ notin \ mathbb {z} $时，只要$ k \ in \ mathbb in \ mathbb in \ mathbb {z z} $。我们的主要结果说，单调多莫诺群的晶格$（M \ times n）$ - 矩形的覆盖率最少，是$ \ weft \ left \ lceil \ frac {2} {3} {3} {3} \ left（m+n- \ sqrt {m+n- \ sqrt {m^2+n^2+n^2+n^2+n^2+n^2+n^2 mn} \右）该论文是出于在棋盘上直线排列的问题而动机。
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.
