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dc.contributor.authorCurrie, James D.
dc.contributor.authorBlanchet-Sadri, Francine
dc.contributor.authorFox, Nathan
dc.contributor.authorRampersad, Narad
dc.date.accessioned2019-12-09T23:39:37Z
dc.date.available2019-12-09T23:39:37Z
dc.date.issued2016-02-14
dc.identifier.citationElectronic Journal of Combinatorial Number Theory 14 (2014), A11en_US
dc.identifier.urihttp://hdl.handle.net/10680/1759
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 \Theta(n); in fact, it is bounded by 10/3 n 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(logn) with constant approaching 3/4 (assuming base 2 logarithm), and it is \Omega(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.urimath.colgate.edu/~integers/vol14.htmlen_US
dc.language.isoenen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectThue-Morse, vtm, Abelian complexity, morphism, nonrepetitiveen_US
dc.titleAbelian complexity of fixed point of morphism 0 -> 012, 1 -> 02, 2 -> 1en_US
dc.typeArticleen_US
dc.identifier.doimath.colgate.edu/~integers/vol14.htmlen_US


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