Re: Re: generating submultisets with repeated elements

*To*: mathgroup at smc.vnet.net*Subject*: [mg103827] Re: [mg103806] Re: generating submultisets with repeated elements*From*: David Bevan <david.bevan at pb.com>*Date*: Thu, 8 Oct 2009 07:50:51 -0400 (EDT)*References*: <ha4r9k$d0h$1@smc.vnet.net> <200910071101.HAA00387@smc.vnet.net>

That's an interesting bijection I wasn't aware of. Thanks. David %^> > -----Original Message----- > From: monochrome [mailto:bayard.webb at gmail.com] > Sent: 7 October 2009 12:02 > To: mathgroup at smc.vnet.net > Subject: [mg103806] Re: generating submultisets with repeated elements > > I did a little research and found out that there are Choose(n+k-1, k) > multisets of size k from a set of size n. This made me think that > there should be a mapping from the k-subsets of n+k-1 to the k- > multisets of n. A few quick examples led me to the following function: > > f[set_] := Table[set[[i]] - (i - 1), {i, Length[set]}] > > This allows the following construction using the KSubsets function > from Combinatorica: > > << "Combinatorica`"; > n = 6; > k = 3; > set = Range[n + k - 1]; > Map[f, KSubsets[set, k]] > > ===OUTPUT=== > {{1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}, {1, 1, 5}, {1, 1, 6}, {1, > 2, 2}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 2, 6}, {1, 3, 3}, {1, > 3, 4}, {1, 3, 5}, {1, 3, 6}, {1, 4, 4}, {1, 4, 5}, {1, 4, 6}, {1, 5, > 5}, {1, 5, 6}, {1, 6, 6}, {2, 2, 2}, {2, 2, 3}, {2, 2, 4}, {2, 2, > 5}, {2, 2, 6}, {2, 3, 3}, {2, 3, 4}, {2, 3, 5}, {2, 3, 6}, {2, 4, > 4}, {2, 4, 5}, {2, 4, 6}, {2, 5, 5}, {2, 5, 6}, {2, 6, 6}, {3, 3, > 3}, {3, 3, 4}, {3, 3, 5}, {3, 3, 6}, {3, 4, 4}, {3, 4, 5}, {3, 4, > 6}, {3, 5, 5}, {3, 5, 6}, {3, 6, 6}, {4, 4, 4}, {4, 4, 5}, {4, 4, > 6}, {4, 5, 5}, {4, 5, 6}, {4, 6, 6}, {5, 5, 5}, {5, 5, 6}, {5, 6, > 6}, {6, 6, 6}} >

**References**:**Re: generating submultisets with repeated elements***From:*monochrome <bayard.webb@gmail.com>