Re: A special kind of partitions of an integer

• To: mathgroup at smc.vnet.net
• Subject: [mg48161] Re: A special kind of partitions of an integer
• From: "Rob Pratt" <Rob.Pratt at sas.com>
• Date: Fri, 14 May 2004 20:59:25 -0400 (EDT)
• References: <200405131305.JAA24791@smc.vnet.net> <c81hq6\$4uc\$1@smc.vnet.net>
• Reply-to: "Rob Pratt" <Rob.Pratt at sas.com>
• Sender: owner-wri-mathgroup at wolfram.com

```"Cezar Augusto de Freitas Anselmo" <cafa at ime.unicamp.br> wrote in message
news:c81hq6\$4uc\$1 at smc.vnet.net...
> Dear friends,
>
>  I'm looking in literature theory of certain partitions of a integer.
>
>  Have you worked with partitions of a integer n in n terms where the
>  summation is not associative (or know someone or texts about it, or
>  other discussion list)?
>
>  Example:
>  I have to count P(n): the number of partitions of n with n positive
>  integers (the only so integer is one) terms where the + operator is not
>  associative, but is commutative; but the recurrence isn't simple. See
>  below
>
>  2 = (1+1);
>  (thus P(2)=1)
>  3 = ((1+1)+1);
>  (thus P(3)=1)
>  4 = (((1+1)+1)+1), ((1+1)+(1+1));
>  (thus P(4)=2)
>  = ((((1+1)+1)+1)+1), (((1+1)+(1+1))+1), (((1+1)+1)+(1+1));
>  (thus P(5)=3)
>
>
>  P(6)=6
>  P(7)=11
>
>  Thanks for all help,
>
>  --
>  ========================================
>  Cézar Freitas (ICQ 109128967)
>  IMECC - UNICAMP / IME - USP
>  Campinas / São Paulo, SP - Brasil

http://www.research.att.com/projects/OEIS?Anum=A001190

Rob Pratt

```

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