The visually distinct configurations of k sets

James F. Lynch
1981 Discrete Mathematics  
Two sets of sets, Co and C" are said to be visually equivalent if there is a l-l mapping m from C" onto C, such that for every S, TE Co, S n T= $1 if and only if m( S1 n m(T) = pl and S c 7' if and only if m(S) c m(T). We find estimates for V(k), the number of equivalence classes of this relation on sets of k sets, for finite and infinite k. Our main results are that for finite k, $k' -k log k <log V(k)<ah'+ fJk +'log k, where (Y and B are appz:oximately 0.7255 and 2.5323 respectively, and
more » ... is a set N of cardinality jf k* t k) such that there are V(k) visually d?stinct sets of k subsets of N.
doi:10.1016/0012-365x(81)90272-7 fatcat:tkoc3lfk3vb3zhmaxibgx2olyy