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Search: id:A130306
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| A130306 |
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Degree of the scheme of n X n complex matrices that square to zero. |
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+0
5
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| 2, 2, 12, 28, 440, 2456, 98448, 1327632, 134302752, 4398726432, 1116577758912, 89104889764288
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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A. Knutson and P. Zinn-Justin, A scheme related to the Brauer loop model, Adv. in Math. 214 (2007), 40-77.
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FORMULA
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a(2n)=2^n det(binomial(2i+2j+1,2i)), 0<=i,j<=n-1 a(2n+1)=2^(n+1) det(binomial(2i+2j+3,2i+1)), 0<=i,j<=n-1
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EXAMPLE
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in size 1, the scheme {x^2=0} is of degree 2. in size 2, the scheme of matrices {{m11,m12},{m21,m22}} that square to zero is generically reduced and the corresponding reduced scheme is given by the equations m11+m22=0 and m11^2+m12 m21=0, hence also of degree 2.
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CROSSREFS
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Cf. A130294.
Sequence in context: A137782 A131384 A052612 this_sequence A093044 A033886 A087131
Adjacent sequences: A130303 A130304 A130305 this_sequence A130307 A130308 A130309
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KEYWORD
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nonn
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AUTHOR
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Paul Zinn-Justin (pzinn(AT)lptms.u-psud.fr), Aug 06 2007
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