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

[Jean-François Alcover]

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/>>
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