Measure preserving words are primitive
نویسندگان
چکیده
منابع مشابه
Measure Preserving Words Are Primitive
The word w is called measure preserving with respect to a finite group G if all the fibers of this map are of equal size. Namely, every element in G is obtained by substitutions in w the same number of times. We say that w is measure preserving if it is measure preserving w.r.t. every finite group. The last years have seen a great interest in word maps in groups, and the distributions they indu...
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A word is called primitive if it cannot be expressed as the power of another word. Morphisms preserving primitive words are investigated. Similarly to the word case, each square-free morphism is a primitive morphism but the converse does not hold. A precise characterization of primitive morphisms is provided in terms of pure codes. An easily testable characterization is given for uniform morphi...
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We introduce the concept of unavoidability of languages with respect to a language class; this means that every language of the given class shares at least some word with the unavoidable language. Several examples of such unavoidabilities are presented. The most interesting one is that the set of primitive words is unavoidable for context-free languages that are not linear. 1 The Language of Pr...
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متن کاملAbelian Primitive Words
We investigate Abelian primitive words, which are words that are not Abelian powers. We show the set of Abelian primitive words is not context-free. We can determine whether a word is Abelian primitive in linear time. Also different from classical primitive words, we find that a word may have more than one Abelian root. We also consider enumeration of Abelian primitive words.
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2014
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2014-00796-7