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Search: id:A098705
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| A098705 |
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Coefficients in a certain Poincare series. |
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+0
4
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| 1, 1, 0, 0, 1, 2, 2, 2, 4, 7, 9, 12, 20, 32, 45, 66, 105, 164, 246, 372, 582, 909, 1393, 2146, 3355, 5240, 8132, 12660, 19825, 31051, 48554, 76038, 119409, 187635, 294760, 463520, 729980, 1150296, 1813100, 2859948, 4515225, 7132412
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Let V=Sum_{k=1..infty} V_k be the graded vector space H_*(PC^infty)[1], which has Poincare series p(t)=t/(1-t^2). Let L be the free graded Lie algebra V. There is a graded involution theta on V induced by an involution on PC^infty, which acts on V_{2k+1} as (-1)^k. The sequence gives the dimensions of the +1-eigenspaces of theta on the graded components of L.
Lehrer-Segal give a recurrence; both this reference and the Lehrer article give the first 50 terms.
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REFERENCES
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G. I. Lehrer and G. B. Segal, Homology stability for classical regular semisimple varieties, Math. Zeit., 236 (2001), 251-290; p. 285.
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LINKS
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G. I. Lehrer, Some sequences arising at the interface of representation theory and homotopy theory
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CROSSREFS
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Adjacent sequences: A098702 A098703 A098704 this_sequence A098706 A098707 A098708
Sequence in context: A000799 A063823 A005865 this_sequence A029866 A077943 A077993
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Oct 28 2004
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