Interval variety: Difference between revisions
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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. | ||
== Facts == | |||
=== Abstractly SV4 scale patterns === | |||
* There exist no 6-letter abstractly SV4 words. | |||
* There exist 3 7-letter abstractly SV4 words: '''0123210''', '''0102013''', and '''3102010'''. The last two patterns are a chiral pair. | |||
* There exist 2 8-letter abstractly SV4 words: '''00100232''' and '''01212103'''. | |||
* There exist no 9-letter abstractly SV4 words. | |||
== Open questions == | == Open questions == | ||
* Why are (abstractly) SV4 circular words seemingly so rare? | * Why are (abstractly) SV4 circular words seemingly so rare? | ||