Fraenkel word: Difference between revisions

'''Fraenkel's conjecture''' asserts that the only balanced circular words over ''n'' &ge; 3 letters with letter occurrences pairwise distinct are (letter reassignments of) <math>F_n.</math><ref>Bulgakova, D. V., Buzhinsky, N., & Goncharov, Y. O. (2023). On balanced and abelian properties of circular words over a ternary alphabet. Theoretical Computer Science, 939, 227-236.</ref> In particular, it implies that the only balanced primitive circular words over at least 3 letters that have "step count vectors" with pairwise distinct components are Fraenkel words. The conjecture is known to be true for [[arity]] 3 to 7.