Theoretical and Practical Aspects Related to the Avoidability of Patterns in Words

Studying avoidability of patterns has long-established roots and has been performed by renowned scholars. Studies of this nature can be traced back over one hundred years. This thesis concerns repetitive structures in words. More precisely, it contributes to studying appearance and absence of such repetitions in words. In the first and major part of this thesis, we study avoidability of unary patterns with permutations.The second part of this thesis deals with modeling and solving several avoidability problems. Representing the problem-based SAT solvers seemed to be a standardised, and usually very optimised approach to formulate and solve the well-known avoidability problems. The final part is concerned with a variation on aclassical avoidance problem from combinatorics on words. We find the supremum of powers that can be constructed by concatenation of different factors of the word w.




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