🚀 go-pugleaf

Mike Robson writes

> Who can shoot down this alleged proof that P=NP?
  [...]
> Claim 2: If T is a solution to $LP$, it covers a permutation vector
> $Q sub pi$.

Maybe I can.  The T matrix displayed in section 3 of Gismondi and Swart's
isomorphism paper (sept 1992) covers no permutation vector.  (There
are only 24, so you can check by brute force, if you want.)

Claim 2, if true, would imply that the feasible region for Robson's
linear programming problem had precisely the set of permutation vectors
as its extreme points.  This is clearly out of step with the discussion
in G&S section 3.  I think G&S introduce their whole rigamarole of U vectors
and actions of permutations on triples of symbols to get around this
problem.