Abstract:Let H and K be subsets of the vertex set V (Q d ) of the d-cube Q d (we call H and K configurations in Q d ). We say K is an exact copy of H if there is an automorphism of Q d which sends H to K. If d is a positive integer and H is a configuration in Q d , we define π(H, d) to be the limit as n goes to infinity of the maximum fraction, over all subsets S of V (Q n ), of sub-d-cubes of Q n whose intersection with S is an exact copy of H. We determine π(C 8 , 4) and π(P 4 , 3) where C 8 is a "perfect" 8-cycle in… Show more
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