Weinbaum’s conjecture on unique subwords of nonperiodic words
Andrew J. Duncan, James Howie · Proceedings of the American Mathematical Society · 1992
Following a conjecture of Weinbaum, we show that every nonperiodic word W W of length at least 2 in a free group has a cyclic permutation of the form UV , where each of U U and V V occur precisely once as a cyclic subword of W W and neither occurs as a cyclic subword of W − 1 {W^{ - 1}} . In fact, we prove a somewhat stronger version of this result and also give a number of applications to one-relator products of groups.