partition

*To*: mathgroup at smc.vnet.net*Subject*: [mg8825] partition*From*: " (Fred Lang)" <lang at einev.ch>*Date*: Mon, 29 Sep 1997 02:39:50 -0400*Sender*: owner-wri-mathgroup at wolfram.com

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.