[seqfan] Re: A095814

T. D. Noe noe at sspectra.com
Fri Jun 7 21:13:48 CEST 2013


I suggest adding a comment to the sequence about your findings. The author
could be contacted.

Tony

At 2:14 PM -0400 6/7/13, Allan Wechsler 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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