AN EXPLICIT 1-FACTORIZATION IN THE MIDDLE OF THE BOOLEAN LATTICE

An explicit definition of a 1-factorization of B(k) (the bipartite gra ph defined by the k- and (k + 1)-element subsets of [2k + 1]), whose c onstituent matchings are defined using addition modulo k + 1, is intro duced. We show that the matchings are invariant under rotation (mappin g under sigma = (1, 2, 3, ..., 2k + 1)), describe the effect of reflec tion (mapping under rho = (1, 2k + 1)(2, 2k) ... (k, k + 2)), determin e that there are no other symmetries which map these matchings among t hemselves, and prove that they are distinct from the lexical matchings in B(k). (C) 1994 Academic Press, Inc.