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A213090
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Number of permutations of length n whose associated Schubert variety is defined by inclusions.
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1
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1, 1, 2, 6, 23, 101, 477, 2343, 11762, 59786, 306132, 1574536, 8120782, 41957030, 217021682, 1123371986, 5817788471, 30139492189, 156174965473, 809382185187, 4195096032623, 21745137658765, 112720985668763, 584336632836945, 3029232133574325, 15703985220888071
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OFFSET
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0,3
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COMMENTS
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Permutations avoiding the four permutation patterns 4231, 35142, 42513, 351624.
See references for several other characterizations.
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REFERENCES
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V. Gasharov and V. Reiner, Cohomology of smooth Schubert varieties in partial flag manifolds, J. Lond. Math. Soc. 66 (2002), 550-562.
A. Hultman, S. Linusson, J. Shareshian, and J. Sjöstrand, From Bruhat intervals to intersection lattices and a conjecture of Postnikov, J. Combin. Theory Ser. A, 116(3) (2009), 564-580.
S. Oh, A. Postnikov and H. Yoo, Bruhat order, smooth Schubert varieties, and hyperplane arrangements, J. Combin. Theory Ser. A 115(7) (2008), 1156-1166.
J. Sjöstrand, Bruhat intervals as rooks on skew Ferrers boards, J. Combin. Theory Ser. A 114 (2007), 1182-1198.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..500
M. H. Albert and R. Brignall, Enumerating indices of Schubert varieties defined by inclusions, arXiv:1301.3188 [math.CO] - Michael Albert, Jan 15 2013
A. Postnikov, Total positivity, Grassmannians, and networks, arXiv:math/0609764v1
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FORMULA
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G.f.: 1 + (1-3*x-2*x^2-(1-x-2*x^2)*sqrt(1-4*x)) / (1-3*x-(1-x+2*x^2) * sqrt(1-4*x)). - Michael Albert, Jan 15 2013
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CROSSREFS
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Sequence in context: A133656 A078487 A193038 * A218225 A120346 A050389
Adjacent sequences: A213087 A213088 A213089 * A213091 A213092 A213093
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KEYWORD
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nonn
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AUTHOR
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Joel B. Lewis, Jun 05 2012
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STATUS
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approved
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