[seqfan] Re: A095814
T. D. Noe
noe at sspectra.com
Fri Jun 7 19:07:29 CEST 2013
Not sure what you mean by your last paragraph. This sequence will be kept.
We do not not delete sequences that are this old.
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
>> > 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
>> > 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
>> > 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
>> > 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
>> > 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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