Minimal enumerations of subsets of a finite set and the middle level problem

A well-known problem of the existence of a Hamilton cycle in the middle two levels of the n-dimensional Boolean lattice, n is odd, is considered. The necessary and sufficient conditions for an n-symbol sequence to be a code o f the cycle are obtained. It is shown that symbols of the sequence must sat isfy certain properties of an uniform distribution in the sequence. (C) 200 1 Elsevier Science B.V. All rights reserved.