Re: compositions with the restricted set of integers

*To*: mathgroup at smc.vnet.net*Subject*: [mg105177] Re: [mg105143] compositions with the restricted set of integers*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Mon, 23 Nov 2009 06:53:22 -0500 (EST)*References*: <200911221110.GAA10476@smc.vnet.net>

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}]]]; For example: In[2]: = outsNew[53, 25] // Timing Out[2] = {0.05, 247679998965100} Regards, Leonid On Sun, Nov 22, 2009 at 3:10 AM, michael partensky <partensky at gmail.com>wrote: > IntegerPartitions has a useful option restricting the values of > partitions. > For example, IntegerPartitions[6,2,{1,2,3,4,5,6}] . Does it exist for > Compositions? > > What I am looking for is a substitute for a lengthy and inefficient > approach described below. We through n dice. How many outcomes > *outs*correspond to the face total equal > *sum*? > I am aware about the recursive approach, but prefer to describe it in terms > of integer partitioning (or compositions). > *Here is my intellectually insulting solution:* > > outs[sum_, thr_] := > Length[Flatten[ > Permutations /@ > Cases[IntegerPartitions[sum, thr, {1, 2, 3, 4, 5, 6}], > Table[_, {thr}]], 1]]; > > Mapping with permutations seems especially silly. > Is there a version of Compositions with the similar restrictive option ({1, > 2, 3, 4, 5, 6})? > I would appreciate any other suggestions as well. > > Thanks > Michael > > >

**References**:**compositions with the restricted set of integers***From:*michael partensky <partensky@gmail.com>