Fraenkel word: Difference between revisions
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</math> | </math> | ||
== Open problems == | == Open problems == | ||
'''Fraenkel's conjecture''' implies that the only 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. | '''Fraenkel's conjecture''' asserts that the only balanced infinite words (periodic or not) over ''n'' letters with letter densities pairwise distinct are eventually (letter reassignments of) infinite repetitions of <math>F_n.</math><ref>R. Tijdeman, | ||
Fraenkel's conjecture for six sequences, | |||
Discrete Mathematics, | |||
Volume 222, Issues 1–3, | |||
2000, | |||
Pages 223-234, | |||
ISSN 0012-365X, | |||
https://doi.org/10.1016/S0012-365X(99)00411-2. | |||
(https://www.sciencedirect.com/science/article/pii/S0012365X99004112)</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. | |||
[[Category:Terms]] | [[Category:Terms]] | ||