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//*********************************************
// MISC COMBINATORIAL FUNCTIONS:
// Given a set S, return the set of lists of the form `[A,B]`, where A,B are disjoint
// two element subsets of S. (Note [A,B] ne [B,A].)
function PairsOfOrderedPairs(S)
subs := Subsets(S,2);
function PairListsWithPrefix(a)
J := S diff a;
subs_next := Subsets(J,2);
return { [a,b] : b in subs_next};
end function;
return &join [PairListsWithPrefix(a) : a in subs];
end function;
// Given a set `S` of size 6, return the different ways of writing S as a disjoint union
// S = A join B of 3-element subsets.
function BalancedPartitionOfSixEltSet(S)
assert #S eq 6;
subs := Subsets(S,3);
return { { a, S diff a} : a in subs };
end function;
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