Glossary for combinatorics on words: Difference between revisions
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The latter definition fails to distinguish primitive circular words from nonprimitive ones. |
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| conjugate || equivalent under modal rotation || Words ''u'' and ''v'' are conjugate if there exist words ''s'' and ''t'' such that ''u'' = ''st'' and ''v'' = ''ts''. Compare: any two group elements of the form ''st'' and ''ts'' are also conjugate. | | conjugate || equivalent under modal rotation || Words ''u'' and ''v'' are conjugate if there exist words ''s'' and ''t'' such that ''u'' = ''st'' and ''v'' = ''ts''. Compare: any two group elements of the form ''st'' and ''ts'' are also conjugate. | ||
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| circular word, necklace || [[periodic scale]] || An equivalence class of words that are conjugate | | circular word, necklace || [[periodic scale]] || An equivalence class of words that are conjugate. | ||
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| factor, subword || || ''u'' is a ''factor'' of ''w'' if ''w = yuv'' for words ''y'' and ''v''. ''u'' is a factor of a circular word [''w''] if it is a factor of some representative of [''w'']. | | factor, subword || || ''u'' is a ''factor'' of ''w'' if ''w = yuv'' for words ''y'' and ''v''. ''u'' is a factor of a circular word [''w''] if it is a factor of some representative of [''w'']. | ||