Plans regarding Ramsey problems.
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Detailed Description
Plans regarding Ramsey problems.
 Todo:
 Relations to other modules
 Todo:
 Automorphisms of Ramsey hypergraphs

First the natural operation of S_n on ramsey_hg(q,r,n) needs to be made available.

Implemented in ComputerAlgebra/RamseyTheory/Lisp/Ramsey/Hypergraphs.mac.

Easiest first to consider the elements of S_n as lists.

The operation of S_n should be faithful (in most cases), and we need to extract the induced automorphisms of ramsey_hg(q,r,n).

Then we need to find out whether these automorphisms cover all.

For small parameters values (including q=3,r=2) we can enumerate all automorphisms by brute force.

What tools are available for hypergraph automorphisms?

It would also be interesting here to try apply some of the symmetry breaking ideas discussed in Satisfiability/Lisp/Generators/RamseyTheory/plans/RamseyProblems.hpp and then consider the number and character of the remaining symmetries.
 Todo:
 Automorphisms of Ramsey clausesets

The obvious automorphisms of diagonal Ramsey clausesets are given by the inner product of automorphisms for the underlying Ramsey hypergraph and the S_s when using s colours.

So at least we have S_n x S_s (translated).

Are there more?

It seems that by brute force (enumerating all clauseset automorphisms we cannot process any nontrivial example?

We need stronger tools for computing automorphisms of clausesets.

And what about nondiagonal Ramsey clausesets? One would guess that in "most" cases there are no other automorphisms than given by the underlying S_n ?
 Todo:
 Representing counterexamples
Definition in file general.hpp.