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 == | == Facts == | ||
Theorem: for all ''n'' ≥ 1, the word '''0123'''...('''''n''-1''')'''n''' is SV''n''. | |||
<!-- prove this --> | |||
=== Abstractly SV4 scale patterns === | === Abstractly SV4 scale patterns === | ||
Abstractly SV4 scale patterns (patterns that are SV4 for any choice of distinct cent values for the four steps): | Abstractly SV4 scale patterns (patterns that are SV4 for any choice of distinct cent values for the four steps): | ||