[seqfan] Re: A095814

Tw Mike mt.kongtong at gmail.com
Fri Jun 7 09:34:33 CEST 2013


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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