Fraenkel word: Difference between revisions
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Here ε is the empty word. Fraenkel words are frequently encountered as sporadic examples of scale properties, such as [[maximum variety]] 3 and [[balance]]. | |||
Fraenkel words are named after mathematician Aviezri S. Fraenkel. | |||
== Facts == | == Facts == | ||
Below we denote the length of a word ''w'' by |''w''| and the number of occurrences of the letter '''i''' in ''w'' as {{!}}''w''{{!}}<sub>'''i'''</sub>, as is standard notation in combinatorics on words. The notation ''w''(''u''<sub>0</sub>, ..., ''u''<sub>''r''−1</sub>) represents the word ''w'' in '''0''', '''1''', ..., '''r−1''' but with '''i''' replaced by the word ''u''<sub>''i''</sub>. | Below we denote the length of a word ''w'' by |''w''| and the number of occurrences of the letter '''i''' in ''w'' as {{!}}''w''{{!}}<sub>'''i'''</sub>, as is standard notation in combinatorics on words. The notation ''w''(''u''<sub>0</sub>, ..., ''u''<sub>''r''−1</sub>) represents the word ''w'' in '''0''', '''1''', ..., '''r−1''' but with '''i''' replaced by the word ''u''<sub>''i''</sub>. | ||