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Search: id:A165663
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| A165663 |
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Decimal expansion of 3 + sqrt(3), arising in constructing the extended Haagerup planar algebra. |
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+0
1
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| 4, 7, 3, 2, 0, 5, 0, 8, 0, 7, 5, 6, 8, 8, 7, 7, 2, 9, 3, 5, 2, 7, 4, 4, 6, 3, 4, 1, 5, 0, 5, 8, 7, 2, 3, 6, 6, 9, 4, 2, 8, 0, 5, 2, 5, 3, 8, 1, 0, 3, 8, 0, 6, 2, 8, 0, 5, 5, 8, 0, 6, 9, 7, 9, 4, 5, 1, 9, 3, 3, 0, 1, 6, 9, 0, 8, 8, 0, 0, 0, 3, 7, 0, 8, 1, 1, 4, 6, 1, 8, 6, 7, 5, 7, 2, 4, 8, 5, 7, 5, 6, 7, 5, 6, 2
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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Abstract: We construct a subfactor planar algebra, and as a corollary a subfactor, with the 'extended Haagerup' principal graph pair. This is the last open case from Haagerup's 1993 list of potential principal graphs of subfactors with index in the range (4,3+sqrt(3)). We prove that the subfactor planar algebra with these principal graphs is unique. We give a skein theoretic description, and a description as a subalgebra generated by a certain element in the graph planar algebra of its principal graph. We give an explicit algorithm for evaluating closed diagrams using the skein theoretic description. This evaluation algorithm is unusual because intermediate steps may increase the number of generators in a diagram.
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LINKS
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Stephen Bigelow, Scott Morrison, Emily Peters, Noah Snyder, Constructing the extended Haagerup planar algebra, Sep 22, 2009.
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FORMULA
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Equals 4+A160390 = 1+A019973 = 2+A090388 = 3+A002194. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 27 2009]
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EXAMPLE
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4.73205081....
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CROSSREFS
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Sequence in context: A098233 A118823 A118826 this_sequence A100127 A130204 A021215
Adjacent sequences: A165660 A165661 A165662 this_sequence A165664 A165665 A165666
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KEYWORD
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cons,easy,nonn,uned
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 24 2009
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EXTENSIONS
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More digits from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 27 2009
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