[seqfan] Re: A095814

Allan Wechsler acwacw at gmail.com
Fri Jun 7 20:14:41 CEST 2013


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.
> >> >
> >> > _______________________________________________
> >> >
> >> > Seqfan Mailing list - http://list.seqfan.eu/
> >> >
> >>
> >> _______________________________________________
> >>
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> >>
> >
> >_______________________________________________
> >
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>
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