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

[Frank Adams-watters]

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 pm
Subject: [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 enough
for me!)
- not of the formula - but of the uniqueness of the partition maximizing
the  product.
Thanks anyway
jfa

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