Interval variety: Difference between revisions
No edit summary |
|||
| Line 57: | Line 57: | ||
** Conjecture: There are only finitely many SV4/MV4 [[circular word]]s. | ** Conjecture: There are only finitely many SV4/MV4 [[circular word]]s. | ||
** Conjecture: For all ''n'' greater than a sufficiently large ''m'', the longest abstractly SV''n'' word is '''0123'''...('''''n''−2''')('''''n''−1''')('''''n''−2''')...'''3210''', with length 2''n'' - 1. | ** Conjecture: For all ''n'' greater than a sufficiently large ''m'', the longest abstractly SV''n'' word is '''0123'''...('''''n''−2''')('''''n''−1''')('''''n''−2''')...'''3210''', with length 2''n'' - 1. | ||
** | ** The following conjecture may be key to proving the ones above: For a sufficiently long [[arity|ternary]] noncircular 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:Combinatorics on words]] | [[Category:Combinatorics on words]] | ||
[[Category:Scale]] | [[Category:Scale]] | ||