Re: compositions with the restricted set of integers

*To*: mathgroup at smc.vnet.net*Subject*: [mg105213] Re: compositions with the restricted set of integers*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Tue, 24 Nov 2009 05:50:58 -0500 (EST)

On 11/23/09 at 6:53 AM, lshifr at gmail.com (Leonid Shifrin) wrote: >Hi, Michael. >Your solution is indeed very memory - hungry due to the mapping of >Permutations, as you mentioned. The total number of permutations can >be easily deduced from the list of multiplicities of elements in a >given partition: n!/(n1!n2!...nk!), where n1, ..., nk are >multiplicities of elements, and n is the length of the partition: >n=n1+...+nk. The multiplicities can be obtained by Tally. The >following modification can be realistically used in a much wider >region of the problem's parameter space than your original one, and >may possibly serve your needs. >In[1]:= >Clear[outsNew]; >outsNew[sum_, thr_] := >Total[Factorial[Length[#]]/ >Times @@ Factorial[Tally[#][[All, 2]]] & /@ >Cases[IntegerPartitions[sum, thr, {1, 2, 3, 4, 5, 6}], >Table[_, {thr}]]]; The above can be made more efficient by using the form of IntegerPartitions that only generates partitions of a given length. That is outs[sum_, thr_] := Total[Factorial[Length[#]]/ Times @@ Factorial[Tally[#][[All, 2]]] & /@ IntegerPartitions[sum, {thr}, {1, 2, 3, 4, 5, 6}]] does the same thing a bit more efficiently