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{{theorem|contents=For all ''n'' ≥ 1, the word '''0123'''...('''''n''-2''')('''''n''-1''')('''''n''-2''')...'''3210''' is SV''n''.}} | {{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|contents=We prove this by dividing this word into four overlapping noncircular subwords which cover all cases. | ||
Consider the subwords '''0123'''...('''''n''-2''')('''''n''-1''') and ('''''n''-1''')('''''n''-2''')...'''3210'''. If we treat these two words as noncircular, then there are ''n''-''k'' distinct ''k''-letter subwords. | Consider the subwords '''0123'''...('''''n''-2''')('''''n''-1''') and ('''''n''-1''')('''''n''-2''')...'''3210'''. If we treat these two words as noncircular, then there are ''n''-''k'' distinct ''k''-letter subwords. | ||