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partition


Dear MathGroup users,
I've the following partition's problem (it's coming from organization of
champions' chip of basket):

Let f = {1,2,3...,n} and e = {{1,2},{1,3},...{n-1,n}} be the set of pairs
of distinct elements of f.

Let's call "admissible" a subset e1 of e which is a 2-partition of f.

Example: n = 6.
{{1,2},{3,4},{5,6}} and  {{1,2},{3,5},{4,6}} are admissible subsets of
{{1,2},{1,3},...{5,6}}.

Problem:

How can I construct a (n-1)-partition of e in admissible subsets?

Example: n = 6.

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

is such a partition.




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