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

[cwwuieee]

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 partsLe 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 -> http://list.seqfan.eu/--Seqfan Mailing list - http://list.seqfan.eu/>> --> Seqfan Mailing list - http://list.seqfan.eu/>--Seqfan Mailing list - http://list.seqfan.eu/