Glossary for combinatorics on words: Difference between revisions

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| Sturmian word || aperiodic MOS scale || An infinite binary word which has exactly (''n'' + 1) distinct length-''n'' subwords for every n ≥ 1.

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| Christoffel word || brightest mode of a periodic [[MOS scale]] || If ''p'' and ''q'' are relatively prime positive integers, then the ''Christoffel word'' of slope ''p''/''q'' is a word ''w'' of length ''p'' + ''q'' defined by ''w''[i] = ''x'' if ''ip'' mod ''n'' > (''i'' − 1)''p'' mod ''n'', ''y'' otherwise.<ref name="paquin">Geneviève Paquin, On a generalization of Christoffel words: epichristoffel words, Theoretical Computer Science, Volume 410, Issues 38–40, 2009, Pages 3782-3791, ISSN 0304-3975.</ref>

| Christoffel word || brightest mode of a periodic single-period [[MOS scale]] || If ''p'' and ''q'' are relatively prime positive integers, then the ''Christoffel word'' of slope ''p''/''q'' is a word ''w'' of length ''p'' + ''q'' defined by ''w''[i] = ''x'' if ''ip'' mod ''n'' > (''i'' − 1)''p'' mod ''n'', ''y'' otherwise.<ref name="paquin">Geneviève Paquin, On a generalization of Christoffel words: epichristoffel words, Theoretical Computer Science, Volume 410, Issues 38–40, 2009, Pages 3782-3791, ISSN 0304-3975.</ref>

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| episturmian word || || An infinite word ''s'' is ''episturmian'' provided that the set of the factors of ''s'' is closed under reversal and ''s'' has at most one right (equivalently left) special factor of each length.<ref name="paquin"/>

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 | Sturmian word || aperiodic MOS scale || An infinite binary word which has exactly (''n'' + 1) distinct length-''n'' subwords for every n &ge; 1.
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-| Christoffel word || brightest mode of a periodic [[MOS scale]] || If ''p'' and ''q'' are relatively prime positive integers, then the ''Christoffel word'' of slope ''p''/''q'' is a word ''w'' of length ''p'' + ''q'' defined by ''w''[i] = ''x'' if ''ip'' mod ''n'' > (''i'' − 1)''p'' mod ''n'', ''y'' otherwise.<ref name="paquin">Geneviève Paquin, On a generalization of Christoffel words: epichristoffel words, Theoretical Computer Science, Volume 410, Issues 38–40, 2009, Pages 3782-3791, ISSN 0304-3975.</ref>
+| Christoffel word || brightest mode of a periodic single-period [[MOS scale]] || If ''p'' and ''q'' are relatively prime positive integers, then the ''Christoffel word'' of slope ''p''/''q'' is a word ''w'' of length ''p'' + ''q'' defined by ''w''[i] = ''x'' if ''ip'' mod ''n'' > (''i'' − 1)''p'' mod ''n'', ''y'' otherwise.<ref name="paquin">Geneviève Paquin, On a generalization of Christoffel words: epichristoffel words, Theoretical Computer Science, Volume 410, Issues 38–40, 2009, Pages 3782-3791, ISSN 0304-3975.</ref>
 |-
 | episturmian word || || An infinite word ''s'' is ''episturmian'' provided that the set of the factors of ''s'' is closed under reversal and ''s'' has at most one right (equivalently left) special factor of each length.<ref name="paquin"/>