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>{{cn|reason=This is not described in the linked article|date=April 2021}} 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.citation

| last = Hone | first = Andrew N. W.

| doi = 10.1098/rsta.2006.1887

| issue = 1849

| journal = Philosophical Transactions of the Royal Society of London

| mr = 2317901

| pages = 3183–3198

| title = Dodgson condensation, alternating signs and square ice

| volume = 364

| year = 2006| bibcode = 2006RSPTA.364.3183H

}}</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==

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{{Matrix classes}}

[[Category:Matrices (mathematics)]]

[[Category:Enumerative combinatorics]]