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A225798
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The number of idempotents in the Jones (or Temperley-Lieb) monoid on the set [1..n].
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4
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1, 2, 5, 12, 36, 96, 311, 886, 3000, 8944, 31192, 96138, 342562, 1083028, 3923351, 12656024, 46455770, 152325850, 565212506, 1878551444, 7033866580, 23645970022, 89222991344, 302879546290, 1150480017950, 3938480377496, 15047312553918, 51892071842570, 199274492098480, 691680497233180
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OFFSET
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1,2
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COMMENTS
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The Jones monoid is the set of partitions on [1..2n] with classes of size 2, which can be drawn as a planar graph, and multiplication inherited from the Brauer monoid, which contains the Jones monoid as a subsemigroup. The multiplication is defined in Halverson and Ram.
These numbers were produced using the Semigroups (2.0) package for GAP 4.7.
No general formula is known for the number of idempotents in the Jones monoid.
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LINKS
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Attila Egri-Nagy, Nick Loughlin, and James Mitchell Table of n, a(n) for n = 1..30 (a(1) to a(21) from Attila Egri-Nagy, a(22)-a(24) from Nick Loughlin, a(25)-a(30) from James Mitchell)
J. D. Mitchell et al., Semigroups package for GAP.
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PROG
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(GAP) for i in [1..18] do
Print(NrIdempotents(JonesMonoid(i)), "\n");
od;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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