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A371505
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Number of sub-monoids of the monoid of uniform block permutations of size n that contain the symmetric group S_n.
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0
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1, 2, 3, 6, 10, 31, 63, 287, 1099, 8640, 62658, 1546891, 29789119, 2525655957
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OFFSET
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1,2
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COMMENTS
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Also equal to the number of anti-chains in the poset of integer partitions of k not equal to (1^k) where mu < lambda iff mu is coarser than lambda and r(mu) >= r(lambda) where r(lambda) = smallest part of lambda not equal to 1.
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LINKS
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EXAMPLE
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a(3) = 3 because the uniform block permutations of size 3; S_3; and the monoid consisting of S_3 and the element with one block are the only three sub-monoids.
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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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