Interval variety: Difference between revisions
No edit summary |
|||
| Line 58: | Line 58: | ||
** 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. | ||
** Related may be the following conjecture: 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. | ** Related may be the following conjecture: 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:Scale]] | [[Category:Scale]] | ||
[[Category:Interval]] | [[Category:Interval]] | ||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Pages with open problems]] | [[Category:Pages with open problems]] | ||