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Search: id:A061539
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| A061539 |
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Signed permutations in B_n which correspond to smooth Schubert varieties. These permutations avoid the following patterns: (-2 -1) (1 2 -3) (1 -2 -3) (-1 2 -3) (2 -1 -3) (-2 1 -3) (3 -2 1) (2 -4 3 1) (-2 -4 3 1) (3412) (3 4 -1 2) (-3 4 1 2) (4 1 3 -2) (4 -1 3 -2) (4 2 3 1) (4 2 3 -1) (-4 2 3 1). |
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OFFSET
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1,1
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COMMENT
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A signed permutation w corresponds to a matrix with exactly one nonzero entry in each row and column and that entry is either 1 or -1. A signed permutation avoids the pattern (1 2 -3) if no three rows and three columns gives a submatrix with diagonal entries 1 1 -1.
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REFERENCES
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S. C. Billey, Pattern Avoidance and Rational Smoothness of Schubert varieties. Advances in Math, vol. 139 (1998) pp. 141-156.
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EXAMPLE
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a(2) = 7 because there are 8 signed permutations of two elements and there is exactly one bad pattern of length 2.
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CROSSREFS
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Cf. A032351.
Sequence in context: A012855 A150646 A128611 this_sequence A116078 A150647 A150648
Adjacent sequences: A061536 A061537 A061538 this_sequence A061540 A061541 A061542
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KEYWORD
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more,nonn
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AUTHOR
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Sara C. Billey (sara(AT)math.mit.edu), May 15 2001
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