Alternating sign matrix: Difference between revisions

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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 matrix|permutation matrices]] and arise naturally when using [[Dodgson condensation]] to compute a determinant.<ref>{{cncitation
|reason last =This isHone not| describedfirst in= Andrew N. W.
| doi = 10.1098/rsta.2006.1887
| issue = 1849
| journal = Philosophical Transactions of the linkedRoyal articleSociety of London
|date mr = 2317901
| pages = 3183–3198
| title = Dodgson condensation, alternating signs and square ice
| volume = 364
| year =April 20212006}}</ref> 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 P. Robbins|David Robbins]], and Howard Rumsey in the former context.

==Examples==