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Structure of equality sets
Hadravová, Jana ; Holub, Štěpán (advisor) ; Currie, James (referee) ; Masáková, Zuzana (referee)
Title: Structure of equality sets Author: Jana Hadravová Department: Department of Algebra Supervisor: doc. Mgr. Štěpán Holub, Ph.D., Dept. of Algebra Abstract: Binary equality set of two morphisms g, h : ⌃⇤ ! A⇤ is a set of all words w over two-letter alphabet ⌃ satisfying g(w) = h(w). Elements of this set are called binary equality words. One of the important results of research on binary equality sets is the proof of the fact that each binary equality set is generated by at most two words provided that both morphisms g and h are non-periodic. Moreover, if a binary equality set is generated by exactly two words, then the structure of both generators, and therefore of the whole set, is uniquely given. This work presents the results of our research on the structure of binary equality sets with a single generator. Importantly, these generators can be decomposed into simpler structures. Generators which can not be further decomposed are called simple equality words. First part of the presented work describes the structure of simple equality words and introduces their detailed classification. The main result of the first part is a precise characterisation of su ciently large simple equality words. In the second part, the work describes the iterative process which transforms a general generator of a binary...
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Structure of equality sets
Hadravová, Jana ; Holub, Štěpán (advisor) ; Currie, James (referee) ; Masáková, Zuzana (referee)
Title: Structure of equality sets Author: Jana Hadravová Department: Department of Algebra Supervisor: doc. Mgr. Štěpán Holub, Ph.D., Dept. of Algebra Abstract: Binary equality set of two morphisms g, h : ⌃⇤ ! A⇤ is a set of all words w over two-letter alphabet ⌃ satisfying g(w) = h(w). Elements of this set are called binary equality words. One of the important results of research on binary equality sets is the proof of the fact that each binary equality set is generated by at most two words provided that both morphisms g and h are non-periodic. Moreover, if a binary equality set is generated by exactly two words, then the structure of both generators, and therefore of the whole set, is uniquely given. This work presents the results of our research on the structure of binary equality sets with a single generator. Importantly, these generators can be decomposed into simpler structures. Generators which can not be further decomposed are called simple equality words. First part of the presented work describes the structure of simple equality words and introduces their detailed classification. The main result of the first part is a precise characterisation of su ciently large simple equality words. In the second part, the work describes the iterative process which transforms a general generator of a binary...
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