Re: [Q] Generalized Partitions

*To*: mathgroup at smc.vnet.net*Subject*: [mg29971] Re: [mg29942] [Q] Generalized Partitions*From*: BobHanlon at aol.com*Date*: Fri, 20 Jul 2001 03:28:34 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

In a message dated 2001/7/19 4:15:11 AM, jkawczak at math.uncc.edu writes: >do you know of a function in Mathematica that could do the partitioning >of a number into a fixed number of components out of predefined set, >i.e. partition number 10 into the elements from the set {1,3,4,5,6,7,9} >and each partition should have exactly, say, 2 elements. Of course, I >have in mind a much bigger problem. > Needs["DiscreteMath`Combinatorica`"]; partSum1[s_Integer, n_Integer, l_List] := Select[Partitions[s], Length[#]==n && l == Union[l, #]&]; partSum2[s_Integer, n_Integer, l_List] := Select[KSubsets[l, n], (Plus@@#)==s&]; If you intended to allow for duplication of elements then partSum1[10, 2, {1, 3, 4, 5, 6, 7, 9}] {{9, 1}, {7, 3}, {6, 4}, {5, 5}} partSum1[10, 3, {1, 3, 4, 5, 6, 7, 9}] {{6, 3, 1}, {5, 4, 1}, {4, 3, 3}} If duplication is not allowed partSum2[10, 2, {1, 3, 4, 5, 6, 7, 9}] {{1, 9}, {3, 7}, {4, 6}} partSum2[10, 3, {1, 3, 4, 5, 6, 7, 9}] {{1, 3, 6}, {1, 4, 5}} Bob Hanlon Chantilly, VA USA