Re: A special kind of partitions of an integer

• To: mathgroup at smc.vnet.net
• Subject: [mg48181] Re: A special kind of partitions of an integer
• From: drbob at bigfoot.com (Bobby R. Treat)
• Date: Mon, 17 May 2004 03:21:49 -0400 (EDT)
• References: <200405131305.JAA24791@smc.vnet.net> <c81hq6\$4uc\$1@smc.vnet.net> <c83ssk\$m94\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```OOPS! I misunderstood your problem; Rob Pratt has it right.

Bobby

drbob at bigfoot.com (Bobby R. Treat) wrote in message news:<c83ssk\$m94\$1 at smc.vnet.net>...
> The same problem was solved in another thread, a few weeks ago. Also
> look up CatalanNumber in Help; it counts the number of these
> partitions.
>
>
> wolf[{arg_}, op_] := {arg}
> wolf[{args__}, op_] := Flatten[ReplaceList[{args}, {a__, b__} :>
> Outer[
>     op, wolf[{a}, op], wolf[{b}, op], 1]], 2]
>
> wolf[Array[1 &, 5], CenterDot]
>
> Displaying with Plus is a bit tricky:
>
> stringIt[a_, b_] := "(" <> ToString[a] <> "+" <> ToString[b] <> ")"
> List @@ (2 @@ wolf[Array[1 &, 5], List] /. List -> stringIt)
>
> DrBob
>
> 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

```

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