Balanced word: Difference between revisions
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== Generalizations == | == Generalizations == | ||
# If <math> \mathsf{block\_balance}(s) \leq m,</math> then we say that ''s'' is ''m''-'''block-balanced'''{{idiosyncratic}}. | # If <math> \mathsf{block\_balance}(s) \leq m,</math> then we say that ''s'' is ''m''-'''block-balanced'''{{idiosyncratic}}. | ||
# The following stronger property implies but is not equivalent to ''m''-block-balancedness: For every letter ''a'' in ''s'' and every factor of ''s'' of the form ''awa'', any factor ''w' '' in ''s'' such that len(<i>w'</i>) = len(''w'') + ''m'' + 1 satisfies |<i>w'</i>|<sub>a</sub> ≥ |''w''|<sub>a</sub> + 1.<ref>Sano, S., Miyoshi, N., & Kataoka, R. (2004). m-Balanced words: A generalization of balanced words. Theoretical computer science, 314(1-2), 97-120.</ref> | # The following stronger property implies but is not equivalent to ''m''-block-balancedness: For every letter ''a'' in ''s'' and every factor of ''s'' of the form ''awa'', any factor ''w' '' in ''s'' such that len(<i>w'</i>) = len(''w'') + ''m'' + 1 satisfies |<i>w'</i>|<sub>''a''</sub> ≥ |''w''|<sub>''a''</sub> + 1.<ref>Sano, S., Miyoshi, N., & Kataoka, R. (2004). m-Balanced words: A generalization of balanced words. Theoretical computer science, 314(1-2), 97-120.</ref> | ||
== References == | == References == | ||
[[Category:Scale]][[Category:Terms]] | [[Category:Scale]][[Category:Terms]] | ||
[[Category:Combinatorics on words]] | [[Category:Combinatorics on words]] | ||