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Growth of Algebras and Codes
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This dissertation is devoted to the study of the growth of algebras and formal languages. It consists of three parts. The first part is devoted to the growth of finitely presented quadratic algebras. The study of these algebras was motivated by the question about the growth types of Koszul algebras which are a special subclass of finitely presented quadratic algebras. We show that there exist finitely presented quadratic algebras of intermediate growth and give two concrete examples of such algebras with their presentations. The second part focuses on the study of the growth of metabelian Lie algebras and their universal enveloping algebras. Our motivation was to construct finitely presented algebras of different intermediate growth types. As an outcome of this investigation we prove that for any d 2 N there exists a finitely presented algebra whose growth function is equivalent to e^n^d=(d+1). The last part focuses on infinite codes over finite alphabets, their properties and growth. A special attention is paid to S-codes, weak S-codes and Markov codes which play an important role in coding theory and ergodic theory. We investigate what types of codes may have maximal growth. Also, we prove that S-codes covering Bernoulli schemes are maximal.
Kocak, Dilber (2016). Growth of Algebras and Codes. Doctoral dissertation, Texas A & M University. Available electronically from