[seqfan] Re: A095814

Allan Wechsler acwacw at gmail.com
Fri Jun 7 21:48:51 CEST 2013


I took T. D. Noe's suggestion and put a comment on Jon Perry's talk page on
OEIS; he seems to check that with reasonable frequency.
https://oeis.org/wiki/User_talk:Jon_Perry#A095814_.22Number_of_nonisomorphic_partitions_of_n_on_the_Ferrers_diagram.22


On Fri, Jun 7, 2013 at 3:24 PM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> I think that the terms and formula should be accepted and the rest should
> be changed accordingly.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
>
> On Fri, Jun 7, 2013 at 2:14 PM, Allan Wechsler <acwacw at gmail.com> wrote:
>
> > I think we are in agreement that various components of this sequence
> > (title, data, comments, formula) are not mutually consistent. What is to
> be
> > done?
> >
> > If we accept the title as authoritative (assuming my interpretation is
> > correct), the sequence will become numerically identical to A005987, and
> > the comments and formula must also be corrected.
> >
> > If we accept the comments as authoritative, then as David Newman pointed
> > out to start this thread, the data are incorrect. I recalculated A(0..10)
> > under these assumptions, and I get A(0)=0 (not 1), a(7)=7, (not 8),
> a(9)=12
> > (not 15), and a(10)=18 (not 21, but agreeing with David's count).  The
> > resulting sequence (0,1,1,2,3,4,6,7,11,12,18) is not currently in OEIS.
> >
> > If we accept the formula as authoritative, it agrees with the data as far
> > as I have checked, but the comments and title must be corrected.
> >
> >
> > On Fri, Jun 7, 2013 at 1:07 PM, T. D. Noe <noe at sspectra.com> wrote:
> >
> > > Not sure what you mean by your last paragraph.  This sequence will be
> > kept.
> > > We do not not delete sequences that are this old.
> > >
> > > Tony
> > >
> > > At 11:28 AM -0400 6/7/13, Allan Wechsler wrote:
> > > >I've tried various interpretations over the last hour and none of them
> > > >generate the numbers given. However, the numbers given *do *seem to
> > > satisfy
> > > >the formula, which is essentially ceil(A000041(n)/2).
> > > >
> > > >What I think happened is that the author was aiming at A005987 and
> > missed.
> > > > (By the way, I find the title there, "symmetric plane partitions", to
> > be
> > > >confusing, but perhaps it is justified by the literature. Comments or
> > > >examples would help.)
> > > >
> > > >If this interpretation is true, then the only reason for keeping
> A095814
> > > is
> > > >that it's ceil(A000041(n)/2).
> > > >
> > > >
> > > >
> > > >On Fri, Jun 7, 2013 at 3:34 AM, Tw Mike <mt.kongtong at gmail.com>
> wrote:
> > > >
> > > >> Dear David,
> > > >> Maybe "nonisomorphic partitions" means "non-self-conjugate
> > partition",so
> > > >> that a(10) = (42-2)/2 =20
> > > >> Yours Mike,
> > > >>
> > > >>
> > > >> 2013/6/7 David Newman <davidsnewman at gmail.com>
> > > >>
> > > >> > I'm still having problems with this sequence, but this time the
> > > problem
> > > >> is
> > > >> > not in the nature of a typographical error.
> > > >> >
> > > >> > We have four sources of knowledge about this sequence, the numbers
> > in
> > > the
> > > >> > sequence itself, the comment, the formula, and the title.  The
> only
> > > ones
> > > >> > which seem to agree are the sequence and the formula.
> > > >> >
> > > >> > The title does not seem clear to me.  It is:  "Number of
> > nonisomorphic
> > > >> > partitions of  n on the Ferres graph".  I take this to mean "the
> > > number
> > > >> of
> > > >> > unrestricted partitions of n up to conjugation," where conjugation
> > is
> > > the
> > > >> > familiar operation of flipping the Ferrers graph so that rows
> become
> > > >> > columns and columns become rows"
> > > >> >
> > > >> > If this is the correct interpretation of the title, then a(n)
> should
> > > be
> > > >> the
> > > >> > number of self-conjugate partitions of n, plus one half the number
> > of
> > > >> > partitions of n which are not self-conjugate.  To give an example:
> > >  The
> > > >> > number of unrestricted partitions of 10 is 42.  There are 2
> > > >> self-conjugate
> > > >> > partitions :52111 and 4321.  So a(10) should be (42-2)/2  +2=22.
> >  But
> > > >> > A095814(10)=21.
> > > >> >
> > > >> > Let's try calculating a(10) using the comment.  The comment reads:
> > > >> > "partitions of n into at most ceil(n/2) parts and with at least
> one
> > > part
> > > >> > greater than or equal to n-floor(n/2)"  For n=10 this becomes
> > > "partitions
> > > >> > of 10 into at most 5 parts and with at least one part greater than
> > or
> > > >> equal
> > > >> > to 5."
> > > >> >
> > > >> > Here is a list of such partitions:
> > > >> >
> > > >> > 1.     10
> > > >> > 2.      91
> > > >> > 3.      82
> > > >> > 4.      811
> > > >> > 5.      73
> > > >> > 6.      721
> > > >> > 7.      7111
> > > >> > 8.      64
> > > >> > 9.      631
> > > >> > 10.     622
> > > >> > 11.     6211
> > > >> > 12.     61111
> > > >> > 13.     55
> > > >> > 14.     541
> > > >> > 15.     532
> > > >> > 16.     5311
> > > >> > 17.     5221
> > > >> > 18.     52111
> > > >> >
> > > >> > This seems to give a(10)=18.
> > > >> >
> > > >> > _______________________________________________
> > > >> >
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> > > >> >
> > > >>
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> > > >>
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