[seqfan] Re: Trying to reach Mitchell Harris, Mma for A056937
Mitch Harris
maharri at gmail.com
Tue Mar 1 17:15:30 CET 2016
Nice! This method with Sage is amazingly fast and makes gfs and recurrence
relations so much easier to discover.
How many then do you want? Yes, all of them, but rather what were you
expecting? And what time-line?
Mitch
On Mon, Feb 29, 2016 at 8:30 AM, Anders Claesson <anders.claesson at gmail.com>
wrote:
> Dear Neil, Mitch and Seq Fans,
>
> I don't have access to Mathematica, but I translated Mitch's program
> into Sage:
>
> C = lambda n: Posets.ChainPoset(n)
> L = lambda n0,n1,n2:
> C(n0).product(C(n1)).product(C(n2)).order_ideals_lattice()
> x = PowerSeriesRing(QQ, 'x', default_prec=40).gen()
>
> zeta = L(2,2,3).mobius_function_matrix().inverse()
> f = ((1 - zeta*x).inverse())[0, zeta.ncols() - 1]
> f.coefficients()
>
> [1,
> 50,
> 887,
> 8790,
> 59542,
> 307960,
> 1301610,
> 4701698,
> 14975675,
> 43025762,
> 113414717,
> 277904900,
> 639562508,
> 1393844960,
> 2896063220,
> 5768600412,
> 11066514565,
> 20526933442,
> 36936277875,
> 64660182026,
> 110394412610,
> 184211567800,
> 300998351550,
> 482402311950,
> 759435697215,
> 1175918169426,
> 1792980231225,
> 2694896131432,
> 3996569551640,
> 5853058431872]
>
> with the small twist that I calculate "all" powers of the zeta-function
> at once in
>
> (1 - zeta*x)^(-1) = 1 + zeta x + zeta^2 x^2 + ...
>
> Instead of doing this calculation in a truncated power series ring (the
> line x = PowerSeriesRing(QQ, 'x', default_prec=40).gen()) one can (very
> slowly) do the same calculation symbolically:
>
> sage: x = var('x')
> sage: f = ((1 - zeta*x).inverse())[0, zeta.ncols() - 1]
> sage: factor(f)
> -(x^6 + 36*x^5 + 279*x^4 + 594*x^3 + 279*x^2 + 36*x + 1)*(x + 1)*x/(x -
> 1)^13
>
> This confirms the empirical formula in A006360.
>
> Cheers,
> Anders
>
> On Thu, Feb 25, 2016, at 04:48 PM, Mitch Harris wrote:
> > I see the problem.
> >
> > JofP and ZetaP are functions provided by an unmentioned package (mea
> > culpa).
> >
> > The package, posets300, is available from Curtis Greene:
> >
> > http://ww3.haverford.edu/math/cgreene/posets.html
> >
> > Mitch
> > --
> > Mitch Harris
> > Cell: 857-636-9981
> > Skype: mitch.harris93
> > LinkedIn: www.linkedin.com/in/mitchharris/
> >
> >
> >
> > On Thu, Feb 25, 2016 at 10:11 AM, Mitch Harris <maharri at gmail.com>
> wrote:
> >
> > > I know how to reach him.
> > >
> > > I'll look into the mma code (though I don't have access to it anymore)
> > >
> > > Mitch
> > >
> > >
> > > On Thu, Feb 25, 2016 at 10:00 AM, Neil Sloane <njasloane at gmail.com>
> wrote:
> > >
> > >> Dear Seq Fans,
> > >> Anyone know how to reach Mitch Harris, former contributor?
> > >>
> > >> The reason is that his Mma progs for A056937, A056933, A056934,
> A056935,
> > >> A056936, A006360, and A006362 don't work
> > >> and it would be nice to extend these sequences.
> > >>
> > >> I've uploaded an annotated copy of the Berman paper, so one can now
> see
> > >> how
> > >> all these seqs are defined.
> > >>
> > >>
> > >> Best regards
> > >> Neil
> > >>
> > >> Neil J. A. Sloane, President, OEIS Foundation.
> > >> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > >> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
> NJ.
> > >> Phone: 732 828 6098; home page: http://NeilSloane.com
> > >> Email: njasloane at gmail.com
> > >>
> > >> --
> > >> Seqfan Mailing list - http://list.seqfan.eu/
> > >>
> > >
> > >
> >
> > --
> > Seqfan Mailing list - http://list.seqfan.eu/
>
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