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Re: Re: Re: generating submultisets with

• To: mathgroup at smc.vnet.net
• Subject: [mg103861] Re: [mg103827] Re: [mg103806] Re: generating submultisets with
• From: David Bevan <david.bevan at pb.com>
• Date: Fri, 9 Oct 2009 07:18:39 -0400 (EDT)
• References: <ha4r9k$d0h$1@smc.vnet.net> <200910071101.HAA00387@smc.vnet.net>

... and using Subsets[set, {k}] is much faster than KSubsets[set, k]


> -----Original Message-----
> From: DrMajorBob [mailto:btreat1 at austin.rr.com]
> Sent: 8 October 2009 17:05
> To: David Bevan; mathgroup at smc.vnet.net
> Cc: bayard.webb at gmail.com
> Subject: Re: [mg103827] Re: [mg103806] Re: generating submultisets with
> repeated elements
>
> g is an improvement over f, I think:
>
> << "Combinatorica`";
>
> Clear[f, g, test1, test2]
> f[set_] := Table[set[[i]] - (i - 1), {i, Length[set]}]
> g[set_] := set - Range[0, Length@set - 1]
> test1[n_, k_] := With[{set = Range[n + k - 1]},
>    f /@ KSubsets[set, k]]
> test2[n_, k_] := With[{set = Range[n + k - 1]},
>    g /@ KSubsets[set, k]]
>
> n = 15; k = 10;
> Timing@Length@test1[n, k]
> Timing@Length@test2[n, k]
> Binomial[n + k - 1, k]
>
> {32.9105, 1961256}
>
> {16.3832, 1961256}
>
> 1961256
>
> Bobby
>
> On Thu, 08 Oct 2009 06:50:51 -0500, David Bevan <david.bevan at pb.com>
> wrote:
>
> > 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}}
> >>
> >
>
>
> --
> DrMajorBob at yahoo.com

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