Interval variety: Difference between revisions
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* Why are (abstractly) SV4 scale patterns seemingly so rare? | * Why are (abstractly) SV4 scale patterns seemingly so rare? | ||
** Conjecture: There are only finitely many SV4 [[circular word]]s of finite length. | ** Conjecture: There are only finitely many SV4 [[circular word]]s of finite length. | ||
** Conjecture: For all ''n'' greater than a sufficiently large ''m'', the longest SV''n'' word is '''0123'''...('''''n'' | ** Conjecture: For all ''n'' greater than a sufficiently large ''m'', the longest SV''n'' word is '''0123'''...('''''n''−2''')('''''n''−1''')('''''n''−2''')...'''3210''', with length 2''n'' - 1. | ||
** Related may be the following conjecture: For a sufficiently long [[arity|ternary]] linear word, there exists ''k'' > 1 such that the interval class of ''k''-steps has at least 3 sizes and the interval class of (''k'' − 1)-steps also has at least 3 sizes. | ** Related may be the following conjecture: For a sufficiently long [[arity|ternary]] linear word, there exists ''k'' > 1 such that the interval class of ''k''-steps has at least 3 sizes and the interval class of (''k'' − 1)-steps also has at least 3 sizes. | ||
[[Category:Scale]] | [[Category:Scale]] | ||