Re: Partition

*To*: mathgroup at smc.vnet.net*Subject*: [mg22101] Re: [mg22091] Partition*From*: BobHanlon at aol.com*Date*: Mon, 14 Feb 2000 02:03:52 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Use the standard add-on package Needs["DiscreteMath`Combinatorica`"] For example, for three variables summing to 10 Without regard to order Select[Partitions[10], Length[#] == 3 &] {{8, 1, 1}, {7, 2, 1}, {6, 3, 1}, {6, 2, 2}, {5, 4, 1}, {5, 3, 2}, {4, 4, 2}, {4, 3, 3}} Length[%] 8 Taking order into count Select[Compositions[10, 3], FreeQ[#, 0] &] {{1, 1, 8}, {1, 2, 7}, {1, 3, 6}, {1, 4, 5}, {1, 5, 4}, {1, 6, 3}, {1, 7, 2}, {1, 8, 1}, {2, 1, 7}, {2, 2, 6}, {2, 3, 5}, {2, 4, 4}, {2, 5, 3}, {2, 6, 2}, {2, 7, 1}, {3, 1, 6}, {3, 2, 5}, {3, 3, 4}, {3, 4, 3}, {3, 5, 2}, {3, 6, 1}, {4, 1, 5}, {4, 2, 4}, {4, 3, 3}, {4, 4, 2}, {4, 5, 1}, {5, 1, 4}, {5, 2, 3}, {5, 3, 2}, {5, 4, 1}, {6, 1, 3}, {6, 2, 2}, {6, 3, 1}, {7, 1, 2}, {7, 2, 1}, {8, 1, 1}} Length[%] 36 Bob Hanlon In a message dated 2/13/2000 2:34:24 AM, kaixiu at students.uiuc.edu writes: >I am wondering how to do a partition work in Mathematica which is like >give all the solutions of >x_1+x_2+x_3+...+x_n=n >where all x's are positive integers and not necessarily be different to >each >other. >