Re: A special kind of partitions of an integer

• To: mathgroup at smc.vnet.net
• Subject: [mg48125] Re: A special kind of partitions of an integer
• From: Cezar Augusto de Freitas Anselmo <cafa at ime.unicamp.br>
• Date: Fri, 14 May 2004 00:12:24 -0400 (EDT)
• References: <200405131305.JAA24791@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

``` 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

```

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