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. > > http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&frame=right&th=ff1de8017f9f5222&seekm=c38uvb%24g39%241%40smc.vnet.net#link2 > > 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