[seqfan] Re: Is a partition with distinct parts and maximum product of parts, unique ?

[Chai Wah Wu]

I should have read the entire thread before replying. As Frank indicated,
the Doslic paper provides the answer to the question. So ignore my comments
above.

Chaiwah

On Fri, Sep 13, 2019 at 8:29 AM cwwuieee <cwwuieee at gmail.com> wrote:

> Then the theorem does not answer your question as the product maximizing
> partition are almost all 3's.
>
> Chaiwah
>
>
>
> -------- Original message --------
> From: Jean-François Alcover <jf.alcover at gmail.com>
> Date: 9/13/19 3:30 AM (GMT-05:00)
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Subject: [seqfan] Re: Is a partition with distinct parts and maximum
> product of parts, unique ?
>
> Ok, but my question was about partitions with distinct parts
>
> Le ven. 13 sept. 2019 à 06:10, cwwuieee <cwwuieee at gmail.com> a écrit :
>
> > The product maximizing partition is not always unique. This is due to 4 =
> > 2+2= 2*2. For instance, for n =7, both the partitions (3,2,2) and (3,4)
> > gives a product of 12.Chaiwah
> > -------- Original message --------From: Frank Adams-watters via SeqFan <
> > seqfan at list.seqfan.eu> Date: 9/12/19  5:21 PM  (GMT-05:00) To:
> > seqfan at list.seqfan.eu Cc: Frank Adams-watters <franktaw at netscape.net>
> > Subject: [seqfan] Re: Is a partition with distinct parts and maximum
> > product of parts, unique ? It's really pretty simple. All of the
> > inequalities in the proof are strict inequalities (> instead of >=). So
> the
> > partition which is found to be optimal is not just >= any other, it is >.
> > And hence it is unique.Franklin T. Adams-Watters-----Original
> > Message-----From: Jean-François Alcover <jf.alcover at gmail.com>To:
> > Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>Sent: Thu, Sep
> > 12, 2019 3:36 pmSubject: [seqfan] Re: Is a partition with distinct parts
> > and maximum product of parts, unique ?Thanks for the link.I feel a bit
> > disappointed there seems to be no simple proof (simple enoughfor me!)-
> not
> > of the formula - but of the uniqueness of the partition maximizingthe
> > product.Thanks anywayjfaLe jeu. 12 sept. 2019 à 21:10, cwwuieee <
> > cwwuieee at gmail.com> a écrit :> Maybe this discussion will help:>
> >
> https://math.stackexchange.com/questions/62201/proof-of-max-product-of-partitions-of-nChaiwah
> >
> > -------- Original message --------From: Jean-François Alcover <>
> > jf.alcover at gmail.com> Date: 9/12/19  1:22 AM  (GMT-05:00) To: Sequence>
> > Fanatics Discussion list <seqfan at list.seqfan.eu> Subject: [seqfan] Is a>
> > partition with distinct parts and maximum product of parts, unique ?
> [This>
> > is about  https://oeis.org/A034893 ]A theorem quoted by Sills &
> > Schneider> :<< Theorem 11 (Anonymous). Among all partitions of n >= 1,the
> > partition> with maximum norm is [...] >>implies it's true, but I'd like
> to
> > get an> explicit proof(a proof I'm unfortunately unable to find !
> ).Thanks
> > in> advance for any help,jfa--Seqfan Mailing list -
> http://list.seqfan.eu/>>
> > --> Seqfan Mailing list - http://list.seqfan.eu/>--Seqfan Mailing list -
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