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Search: id:A082635
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| A082635 |
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Square array read by antidiagonals: degree of the K(2,p)^q variety. |
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| 1, 2, 1, 5, 8, 1, 14, 55, 32, 1, 42, 364, 610, 128, 1, 132, 2380, 9842, 6765, 512, 1, 429, 15504, 147798, 265720, 75025, 2048, 1, 1430, 100947, 2145600, 9112264, 7174454, 832040, 8192, 1, 4862, 657800, 30664890, 290926848, 562110290, 193710244
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numbers are related to the dynamic pole assignment problem. "The variety K(m,p)^q can also be viewed as the parameterization of the space of rational curves of degree q of the Grassmann variety Grass(m,m+p)".
Also lim(n->inf, T(n+1,2i)/T(n,2i)) = 4^(i+1).
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LINKS
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M. S. Ravi et al., Dynamic pole assignment and Schubert calculus, SIAM J. Control Optimization, 34 (1996), 813-832, esp. p. 825.
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FORMULA
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degK2(p, q)=(-1)^q*(2p+pq+2q)!*sum(j=0, q, ((q-2j)(p+2)+1)/(p+j(p+2))!/(p+1+(q-j)(p+2))!).
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EXAMPLE
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Top left corner of array:
1,2,5,14,42,132,429,1430,... A000108 (Catalan numbers)
1,8,55,364,2380,15504,100947,...A013068 deg K(2,n)^1
1,32,610,9842,147798,2145600,...A013069 deg K(2,n)^2
1,128,6765,265720,9112264,... A013070 deg K(2,n)^3
1,512,75025,7174454,... A013071 deg K(2,n)^4
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CROSSREFS
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Cf. A013702.
Second column is A004171(q), third is A000045(5q).
T(n, 2i) = A080934((i+1)n+2i, n+1).
Sequence in context: A014551 A088014 A059274 this_sequence A094510 A023677 A108599
Adjacent sequences: A082632 A082633 A082634 this_sequence A082636 A082637 A082638
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), May 14 2003
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