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dc.contributor.authorBlanchet-Sadri, F.
dc.contributor.authorCurrie, James D.
dc.contributor.authorRampersad, Narad
dc.contributor.authorFox, Nathan
dc.date.accessioned2018-03-16T14:17:22Z
dc.date.available2018-03-16T14:17:22Z
dc.date.issued2014-02-20
dc.identifier.citationF. Blanchet-Sadri, J. Currie, N. Fox, and N. Rampersad. “Abelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1.” Integers 14 (2014): A11.en_US
dc.identifier.issn1867-0652
dc.identifier.urihttp://hdl.handle.net/10680/1408
dc.description.abstractWe study the combinatorics of vtm, a variant of the Thue-Morse word generated by the non-uniform morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1 starting with 0. This infinite ternary sequence appears a lot in the literature and finds applications in several fields such as combinatorics on words; for example, in pattern avoidance it is often used to construct infinite words avoiding given patterns. It has been shown that the factor complexity of vtm, i.e., the number of factors of length n, is Θ(n); in fact, it is bounded by ¹⁰⁄₃n for all n, and it reaches that bound precisely when n can be written as 3 times a power of 2. In this paper, we show that the abelian complexity of vtm, i.e., the number of Parikh vectors of length n, is O(log n) with constant approaching ¾ (assuming base 2 logarithm), and it is Ω(1) with constant 3 (and these are the best possible bounds). We also prove some results regarding factor indices in vtm.en_US
dc.description.sponsorship"F. Blanchet-Sadri and Nathan Fox’s research was supported by the National Science Foundation under Grant No. DMS–1060775." "James D. Currie and Narad Rampersad’s research was supported by NSERC Discovery grants."en_US
dc.language.isoenen_US
dc.publisherIntegersen_US
dc.rightsinfo:eu-repo/semantics/openAccess
dc.titleAbelian complexity of fixed point of morphism 0 ↦ 012, 1 ↦ 02, 2 ↦ 1en_US
dc.typeArticleen_US


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