Interval variety: Difference between revisions
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In the following, two letters are to be considered the same if their numerical values are congruent modulo ''n''. | In the following, two letters are to be considered the same if their numerical values are congruent modulo ''n''. | ||
{{theorem| | {{theorem|contents=For all ''n'' ≥ 1, the word '''0123'''...('''''n''-1''') is SV''n''.}} | ||
{{Proof|contents=All ''k''-letter subwords of '''0123'''...('''''n''-1''') is of the form ('''i''')('''i+1''')...('''i+k-1'''), and there are exactly ''n'' of them.}} | {{Proof|contents=All ''k''-letter subwords of '''0123'''...('''''n''-1''') is of the form ('''i''')('''i+1''')...('''i+k-1'''), and there are exactly ''n'' of them.}} | ||
{{theorem| | {{theorem|contents=For all ''n'' ≥ 1, the word '''0123'''...('''''n''-2''')('''''n''-1''')('''''n''-2''')...'''3210''' is SV''n''.}} | ||
{{Proof|We prove this by dividing this word into four overlapping noncircular subwords which cover all cases. | {{Proof|We prove this by dividing this word into four overlapping noncircular subwords which cover all cases. | ||