ordered pairs

• To: mathgroup at smc.vnet.net
• Subject: [mg7181] ordered pairs
• From: "w.meeussen" <w.meeussen.vdmcc at vandemoortele.be>
• Date: Wed, 14 May 1997 01:11:15 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```hi all,

Is there a predefined function in Mma 3.0 to construct the complete set of
ordered pairs of numbers 1 to n corresponding to the partitions of n in pairs?

example: n=6

Partitions[6,2]
{{2,2,2},{2,2,1,1},{2,1,1,1,1},{1,1,1,1,1,1}}

for the first partition {2,2,2}, I would like all possible combinations:

12 34 56 **
12 35 46 **
12 36 45

13 24 56 **
13 25 46 **
13 26 45

14 23 56
14 25 36 **
14 26 35

15 23 46
15 24 36
15 26 34

16 23 45
16 24 35
16 25 34

where each pair is ordered, and the pairs themselves are ordered according
to the first element.
and analogously for the other partitions.

These are obviously not the Young Tableaux from DiscreteMath`Combinatorica`;
that gives:

Tableaux[{2,2,2}]

{{{1,4},{2,5},{3,6}},
{{1,3},{2,5},{4,6}},
{{1,2},{3,5},{4,6}},
{{1,3},{2,4},{5,6}},
{{1,2},{3,4},{5,6}}}

they are a small subset of what i want, marked with an asterix above.

If there is no pre-defined (combination of) function(s), any hints as to the
way how to tackle this procedurally?

wouter.

Dr. Wouter L. J. MEEUSSEN
eu000949 at pophost.eunet.be
w.meeussen.vdmcc at vandemoortele.be

```

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