A156231 Sequence gives the Poincaré series [or 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.

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

Offset

0,3

References

Stephen P. Humphries, Action of some braid groups on Hodge algebras. Comm. Algebra 26 (1998), no. 4, pages 1233-1242. See Proposition 3.4

Links

Table of n, a(n) for n=0..34.

Stephen P. Humphries, Action of some braid groups on Hodge algebras Comm. Algebra 26 (1998), no. 4, pages 1233-1242. See Proposition 3.4 on page 1241.

Formula

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).

Example

For n=2 the dimension of the degree two part is 6.

Crossrefs

A053090 is a similar Poincaré series [or Poincare series] for a ring on which the three strand braid groups acts.

Sequence in context: A349172 A119875 A053189 * A024860 A025100 A155478

Adjacent sequences: A156228 A156229 A156230 * A156232 A156233 A156234

Keyword

nonn,easy

Author

Stephen P. Humphries, Feb 06 2009

Status

approved