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MathGroup Archive 2004

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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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