Fraenkel word: Difference between revisions
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</math> | </math> | ||
== Open problems == | == Open problems == | ||
'''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''' asserts that the only balanced infinite words (periodic or not) over ''n'' ≥ 3 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, | Fraenkel's conjecture for six sequences, | ||
Discrete Mathematics, | Discrete Mathematics, | ||
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https://doi.org/10.1016/S0012-365X(99)00411-2. | 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. | (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. | ||
== References == | == References == | ||
[[Category:Terms]] | [[Category:Terms]] | ||