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A349457
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Number of singular positroids in the Grassmannian variety Gr(k,n) for a fixed n and any 0 <= k <= n.
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3
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OFFSET
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0,5
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COMMENTS
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a(n) is also the number of decorated permutations whose chordal diagram contains a crossed alignment.
a(n) counts the complement of A349458 in the set of all positroid varieties/decorated permutations on n elements (A000522).
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LINKS
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FORMULA
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a(n) = Sum_{i=0..n} (2^i)*binomial(n,i)*b(n), where b(n) is the sequence A349456.
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EXAMPLE
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For n = 4, the a(4) = 4 singular positroid varieties correspond to the decorated permutations whose underlying permutations are 2413, 3421, 3142, and 4312 in one-line notation. Note that none of these permutations contain fixed points, hence no decorations are needed.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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