Re: Generating r-combination or r-permutations with replacement.

• To: mathgroup at smc.vnet.net
• Subject: [mg51257] Re: [mg51248] Generating r-combination or r-permutations with replacement.
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 10 Oct 2004 05:52:31 -0400 (EDT)
• References: <200410100557.BAA22558@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On 10 Oct 2004, at 14:57, phil wrote:

> Is there an easy function in mathematica that generates a set/list that
> consists of r-combinations or r-permutations with replacement?
>
> e.g. I want the set of all possible sets with 3 elements, with entries
> from
> {1,2,3,4}, and also the set of all possible unordered sets with 3
> elements,
> with entries from {1,2,3,4}.
>
> Any help is appreciated,
>
> -Philip Lu
>
>
>

1.
<< DiscreteMath`Combinatorica`

KSubsets[{1, 2, 3, 4}, 3]

{{1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}

2.

Distribute[Table[{1, 2, 3, 4}, {3}], List]

{{1, 1, 1}, {1, 1, 2}, {1, 1, 3}, {1, 1, 4}, {1, 2, 1},
{1, 2, 2}, {1, 2, 3}, {1, 2, 4}, {1, 3, 1}, {1, 3, 2},
{1, 3, 3}, {1, 3, 4}, {1, 4, 1}, {1, 4, 2}, {1, 4, 3},
{1, 4, 4}, {2, 1, 1}, {2, 1, 2}, {2, 1, 3}, {2, 1, 4},
{2, 2, 1}, {2, 2, 2}, {2, 2, 3}, {2, 2, 4}, {2, 3, 1},
{2, 3, 2}, {2, 3, 3}, {2, 3, 4}, {2, 4, 1}, {2, 4, 2},
{2, 4, 3}, {2, 4, 4}, {3, 1, 1}, {3, 1, 2}, {3, 1, 3},
{3, 1, 4}, {3, 2, 1}, {3, 2, 2}, {3, 2, 3}, {3, 2, 4},
{3, 3, 1}, {3, 3, 2}, {3, 3, 3}, {3, 3, 4}, {3, 4, 1},
{3, 4, 2}, {3, 4, 3}, {3, 4, 4}, {4, 1, 1}, {4, 1, 2},
{4, 1, 3}, {4, 1, 4}, {4, 2, 1}, {4, 2, 2}, {4, 2, 3},
{4, 2, 4}, {4, 3, 1}, {4, 3, 2}, {4, 3, 3}, {4, 3, 4},
{4, 4, 1}, {4, 4, 2}, {4, 4, 3}, {4, 4, 4}}

Andrzej Kozlowski
Chiba, Japan
http://www.akikoz.net/~andrzej/
http://www.mimuw.edu.pl/~akoz/

```

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