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| {{Orphan|date=January 2012}}
| | Hello. Allow me introduce the writer. Her title is Refugia Shryock. What I love doing is playing baseball but I haven't produced a dime with it. California is our beginning place. For years I've been operating as a payroll clerk.<br><br>my website; std testing at home, [http://Xrambo.com/blog/191590 try what he says], |
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| {{Refimprove|date=November 2009}}
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| In [[mathematics]], a '''higher spin alternating sign matrix''' is a generalisation of the [[alternating sign matrix]] ('''ASM'''), where the columns and rows sum to an integer ''r'' (the ''spin'') rather than simply summing to 1 as in the usual alternating sign matrix definition. HSASMs are square matrices whose elements may be integers in the range −''r'' to +''r''. When traversing any row or column of an ASM or HSASM, the partial sum of its entries must always be non-negative.<ref name="ecomjournal">[http://www.combinatorics.org/Volume_14/PDF/v14i1r83.pdf R. E. Behrend and V. A. Knight, "Higher Spin Alternating Sign Matrices", ""The Electronic Journal of Combinatorics"", '''14''' (2007), #R83]</ref>
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| High spin ASMs have found application in [[statistical mechanics]] and [[physics]], where they have been found to represent [[symmetry group]]s in [[ice crystal]] formation.
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| Some typical examples of HSASMs are shown below:
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| :<math>
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| \begin{pmatrix}
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| 0 & 0 & 2 & 0 \\
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| 0 & 2 &-1 & 1 \\
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| 2 &-1 & 2 &-1 \\
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| 0 & 1 &-1 & 2
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| \end{pmatrix};\quad
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| \begin{pmatrix}
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| 0 & 0 & 2 & 0&0 \\
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| 0 & 1 &-1 & 2 &0\\
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| 2 &-1 &-1 & 0 &2\\
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| 0 & 0 & 2 & 0 &0\\
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| 0&2&0&0&0
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| \end{pmatrix};\quad
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| \begin{pmatrix}
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| 0 & 0 & 0 & 2 \\
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| 0 & 2 & 0 & 0 \\
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| 2 &-2 & 2 & 0 \\
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| 0 & 2 & 0 & 0
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| \end{pmatrix};\quad
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| \begin{pmatrix}
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| 0 & 2 & 0 & 0 \\
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| 0 & 0 & 0 & 2 \\
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| 2 & 0 & 0 & 0 \\
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| 0 & 0 & 2 & 0
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| \end{pmatrix}.
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| </math>
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| The set of HSASMs is a [[superset]] of the ASMs. The [[extreme points]] of the [[convex hull]] of the set of ''r''-spin HSASMs are themselves integer multiples of the usual ASMs.
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| ==See also==
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| * [[Sudoku]]
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| ==References==
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| <references />
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| {{DEFAULTSORT:Higher Spin Alternating Sign Matrix}}
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| [[Category:Matrices]]
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| [[Category:Statistical mechanics]]
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| [[Category:Enumerative combinatorics]]
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| {{combin-stub}}
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Latest revision as of 10:06, 1 January 2015
Hello. Allow me introduce the writer. Her title is Refugia Shryock. What I love doing is playing baseball but I haven't produced a dime with it. California is our beginning place. For years I've been operating as a payroll clerk.
my website; std testing at home, try what he says,