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Search: id:A156231
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| A156231 |
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Sequence gives the Poincare series of an ordinal Hodge algebra, or algebra with straightening law, for a ring that the braid group on four strands acts on. It is Cohen-Macaulay |
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1
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| 1, 0, 6, 8, 24, 48, 106, 192, 369, 624, 1080, 1728, 2787, 4248, 6498, 9528, 13962, 19824, 28066, 38760, 53334, 71936, 96618, 127680, 167983, 218040, 281784, 360024, 458037, 577080, 724098, 900936, 1116636, 1373808, 1684038
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Stephen P. Humphries, Action of some braid groups on Hodge algebras. Comm. Algebra 26 (1998), no. 4, pages 1233-1242. See Proposition 3.4
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FORMULA
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G.f. 1-(-4*x^20+8*x^19+6*x^18-12*x^17-11*x^16-2*x^15+25*x^14+10*x^13-12*x^12)/((1+x+x^2)^2*(1+x)^5*(1+x^2)*(1-x)^9)-(-14*x^11-15*x^10+14*x^9+17*x^8+4*x^7-16*x^6-12*x^5+10*x^4+4*x^3-6*x^2)/((1+x+x^2)^2*(1+x)^5*(1+x^2)*(1-x)^9)
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EXAMPLE
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For n=2 the dimension of the degree two part is 6.
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CROSSREFS
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A053090 is a similar Poincare series for a ring on which the three strand braid groups acts.
Adjacent sequences: A156228 A156229 A156230 this_sequence A156232 A156233 A156234
Sequence in context: A005887 A119875 A053189 this_sequence A024860 A025100 A155478
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KEYWORD
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nonn
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AUTHOR
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Stephen Humphries (steve(AT)math.byu.edu), Feb 06 2009
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