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Alternating sign matrix
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Alternating sign matrix : ウィキペディア英語版
Alternating sign matrix

In mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. These matrices generalize permutation matrices and arise naturally when using Dodgson condensation to compute a determinant. They are also closely related to the six-vertex model with domain wall boundary conditions from statistical mechanics. They were first defined by William Mills, David Robbins, and Howard Rumsey in the former context.
==Example==
An example of an alternating sign matrix (that is not also a permutation matrix) is
:
\begin
0&0&1&0\\
1&0&0&0\\
0&1&-1&1\\
0&0&1&0
\end.


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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