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Perfect matrix : ウィキペディア英語版
Perfect matrix
In mathematics, a perfect matrix is an ''m''-by-''n'' binary matrix that has no possible ''k''-by-''k'' submatrix K that satisfies the following conditions:〔D. M. Ryan, B. A. Foster, (''An Integer Programming Approach to Scheduling'' ), p.274, University of Auckland, 1981.〕
* ''k'' > 3
* the row and column sums of K are each equal to ''b'', where ''b'' ≥ 2
* there exists no row of the (''m'' − ''k'')-by-''k'' submatrix formed by the rows not included in K with a row sum greater than ''b''.
The following is an example of a K submatrix where ''k'' = 5 and ''b'' = 2:
::
\begin
1 & 1 & 0 & 0 & 0 \\
0 & 1 & 1 & 0 & 0 \\
0 & 0 & 1 & 1 & 0 \\
0 & 0 & 0 & 1 & 1 \\
1 & 0 & 0 & 0 & 1
\end.

== References ==



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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