Interval variety: Difference between revisions
| Line 11: | Line 11: | ||
Note: A standard academic counterpart to the xen term ''variety'' is the ''abelian complexity function of a [[word]]'': a function ρ<sup>ab</sup> : '''N''' -> '''N''' where ρ<sup>ab</sup>(''n'') is the number of distinct "sizes" that length-''n'' subwords can have in a word. | Note: A standard academic counterpart to the xen term ''variety'' is the ''abelian complexity function of a [[word]]'': a function ρ<sup>ab</sup> : '''N''' -> '''N''' where ρ<sup>ab</sup>(''n'') is the number of distinct "sizes" that length-''n'' subwords can have in a word. | ||
== Open questions == | == Open questions == | ||
* Why are (abstractly) SV4 | * Why are (abstractly) SV4 circular words seemingly so rare? | ||
* Related is the following conjecture: For a sufficiently long ternary circular 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]] | ||
[[Category:Interval]] | [[Category:Interval]] | ||
[[Category:Terms]] | [[Category:Terms]] | ||
[[Category:Articles with open problems]] | [[Category:Articles with open problems]] | ||