[seqfan] Re: Comment on A068982 and The Global Cohen-Lenstra Heuristic

Georgi Guninski guninski at guninski.com
Sun Jan 3 10:43:11 CET 2010

writing about groups, looks like every group that has a map to Z gives a sequence:

start with a generator, apply the group operation n-1 times, map to a(n).
(e.g. linear recurrences with constant coefficients are related to matrix powers and A006769 is closely related to a multiple of a point on EC)

are there other sequences in OEIS resulting from group operations?

On Sat, Jan 02, 2010 at 10:29:23AM -0800, Jonathan Post wrote:
> on p.14 Lengler derives A068982  Limit of the product of a modified
> Zeta function. That hotlink might be added to that sequence.
> http://arxiv.org/PS_cache/arxiv/pdf/0912/0912.4977v1.pdf
>  arXiv:0912.4977 [ps, pdf, other]
>     Title: The Global Cohen-Lenstra Heuristic
>     Authors: Johannes Lengler
>     Subjects: Number Theory (math.NT); Probability (math.PR)
>     The Cohen-Lenstra heuristic is a universal principle that assigns
> to each group a probability that tells how often this group should
> occur "in nature". The most important, but not the only, applications
> are sequences of class groups, which behave like random sequences of
> groups with respect to the so-called Cohen-Lenstra probability
> measure.
>     So far, it was only possible to define this probability measure
> for finite abelian $p$-groups. We prove that it is also possible to
> define an analogous probability measure on the set of \emph{all}
> finite abelian groups when restricting to the $\Sigma$-algebra on the
> set of all finite abelian groups that is generated by uniform
> properties, thereby solving a problem that was open since 1984.
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