[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.

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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