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

Frank Adams-watters franktaw at netscape.net
Fri Sep 13 06:19:37 CEST 2019


You missed or misunderstood the "distinct parts" in the specification. [2,2] does not have distinct parts - both parts are 2.

Franklin T. Adams-Watters


-----Original Message-----
From: cwwuieee <cwwuieee at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Thu, Sep 12, 2019 11:10 pm
Subject: [seqfan] Re: Is a partition with distinct parts and maximum product of parts, unique ?

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/

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