Oldenburg, University, Diss., 2000. / Dateiformat: zip, Dateien in unterschiedlichen Formaten.

Stuttgart, University, Diss., 2003.

This thesis treats combinatorial and topological properties of monoids with absorbing elements and their associated algebras.

PhD / None.

In this paper we discuss what is known so far about diagonal acts of monoids. The first results that will be discussed comprise an overview of some work done on determining whether or not the diagonal act can be finitely generated or cyclic when looking at specific classes of monoids. This has been a topic of interest to a handful of semigroup theorists over the past seven years. We then move on to discuss some results pertaining to flatness properties of diagonal acts. The theory of flatness properties of acts over monoids has been of major interest over the past two decades, but so far there are no papers published on this subject that relate specifically to diagonal acts. We attempt to shed some light on this topic as well as present some new problems.

In this paper we discuss what is known so far about diagonal acts of monoids. The first results that will be discussed comprise an overview of some work done on determining whether or not the diagonal act can be finitely generated or cyclic when looking at specific classes of monoids. This has been a topic of interest to a handful of semigroup theorists over the past seven years. We then move on to discuss some results pertaining to flatness properties of diagonal acts. The theory of flatness properties of acts over monoids has been of major interest over the past two decades, but so far there are no papers published on this subject that relate specifically to diagonal acts. We attempt to shed some light on this topic as well as present some new problems.

<p>This dissertation refines and extends the theory of mesoprimary decomposition, as introduced by Kahle and Miller. We begin with an overview of the existing theory of mesoprimary decomposition </p><p>in both the combinatorial setting of monoid congruences and the arithmetic setting of binomial ideals. We state all definitions and results that are relevant for subsequent chapters. </p><p>We classify redundant mesoprimary components in both the combinatorial and arithmetic settings. Kahle and Miller give a class of redundant components in each setting that are redundant in every mesoprimary decomposition. After identifying a further class of redundant components at the level of congruences, we give a condition on the associated monoid primes that guarantees the existence of unique irredundant mesoprimary decompositions in both settings. </p><p>We introduce soccular congruences as combinatorial approximations of irreducible binomial quotients and use the theory of mesoprimary decomposition to give a combinatorial method of constructing irreducible decompositions of binomial ideals. We also demonstrate a binomial ideal which does not admit a binomial irreducible decomposition, answering a long-standing problem of Eisenbud and Sturmfels. </p><p>We extend mesoprimary decomposition of monoid congruences to congruences on monoid modules. Much of the theory for monoid congruences extends to this new setting, including a characterization of mesoprimary monoid module congruences in terms of associated prime monoid congruences and a method for constructing coprincipal decompositions of monoid module congruences using key witnesses. </p><p>We conclude with a collection of open problems for future study.</p> / Dissertation

PhD / None.

Stuttgart, Univ., Diss., 1996.

Combinatorics on words explore words – often called strings in the com- puter science community, or monoids in mathematics – and their structural properties. One of the most studied question deals with repetitions which are a form of redundancy. The thesis focuses on estimating the maximum number of distinct squares in a string of length n. Our approach is to study the combinatorial properties of these overlapping structures, nested systems, and obtain insights into the intricate patterns that squares create. Determin- ing the maximum number of repetitions in a string is of interest in different fields such as biology and computer science. For example, the question arrises when one tries to bound the number of repetitions in a gene or in a computer file to be data compressed. Specific strings containing many repetitions are often of interest for additional combinatorial properties. After a brief review of earlier results and an introduction to the question of bounding the maxi- mum number of distinct squares, we present the combinatorial insights and techniques used to obtain the main result of the thesis: a strengthening of the universal upper bound obtained by Fraenkel and Simpson in 1998. / Thesis / Doctor of Philosophy (PhD)