Pattern Avoidance
نویسندگان
چکیده
Consider a sequence of letters or numbers. Does a pattern exist that is avoided by the sequence? This topic is a very popular area of research in mathematics for its promising utility in computer science and other branches of mathematics, the elegant proofs and solutions, and the many open problems that still remain. Section 1 of this paper provides definitions, notations, and some properties of pattern avoidance type problem. Section 2 focuses on 132 avoiding patterns and outlines the background and proof for the number of permutations of length n that are 132 avoiding. Section 3 discusses methods to generate circular binary cube-free words. Finally, Section 4 examines methods used to generate words that avoid reversed subwords and details some of the results from work by N. Rampersad and J. Shallit [3].
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