For alphabets Delta_1, Delta_2, a morphism g : Delta_1* to Delta_2* is ambiguous with respect to a word u in Delta_1* if there exists a second morphism h : Delta_1* to Delta_2* such that g(u) = h(u) and g not= h. Otherwise g is unambiguous. Hence unambiguous morphisms are those whose structure is fully preserved in their morphic images. A concept so far considered in the free monoid, the first part of this thesis considers natural extensions of ambiguity of morphisms to free groups. It is shown that, while the most straightforward generalization of ambiguity to a free monoid results in a trivial situation, that all morphisms are (always) ambiguous, there exist meaningful extensions of (un)ambiguity which are non-trivial - most notably the concepts of (un)ambiguity up to inner automorphism and up to automorphism. A characterization is given of words in a free group for which there exists an injective morphism which is unambiguous up to inner automorphism in terms of fixed points of morphisms, replicating an existing result for words in the free monoid. A conjecture is presented, which if correct, is sufficient to show an equivalent characterization for unambiguity up to automorphism. A rather counterintuitive statement is also established, that for some words, the only unambiguous (up to automorphism) morphisms are non-injective (or even periodic). The second part of the thesis addresses words for which all non-periodic morphisms are unambiguous. In the free monoid, these take the form of periodicity forcing words. It is shown using morphisms that there exist ratio-primitive periodicity forcing words over arbitrary alphabets, and furthermore that it is possible to establish large and varied classes in this way. It is observed that the set of periodicity forcing words is spanned by chains of words, where each word is a morphic image of its predecessor. It is shown that the chains terminate in exactly one direction, meaning not all periodicity forcing words may be reached as the (non-trivial) morphic image of another. Such words are called prime periodicity forcing words, and some alternative methods for finding them are given. The free-group equivalent to periodicity forcing words - a special class of C-test words - is also considered, as well as the ambiguity of terminal-preserving morphisms with respect to words containing terminal symbols, or constants. Moreover, some applications to pattern languages and group pattern languages are discussed.

No description available.

Birational morphisms f: X $ to$ Y of nonsingular surfaces are studied first. Properties of the surfaces X and Y are shown to be related to certain numerical data extracted from the configuration of "missing curves" of f, that is, the curves in Y whose generic point is not in f (X). These results are then applied to the problem of decomposing birational endomorphisms of the plane into a succession of irreducible ones. / A graph-theoretic machinery is developed to keep track of the desingularization of the divisors at infinity of the plane. That machinery is then used to investigate the problem of classifying all birational endomorphisms of the plane, and a complete classification is given in the case of two fundamental points.

Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references (leaves 48-49).

Thesis (M.S.)--Rochester Institute of Technology, 1994. / Typescript. Includes bibliographical references (leaf 90).

Thesis (Ph. D.)--University of Missouri-Columbia, 2008. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on June 8, 2009) Vita. Includes bibliographical references.

This thesis is devoted to a problem in the representation theory of the symmetric group over C (the field of the complex numbers). Let d be a positive integer, and let S_d denote the symmetric group on d letters. Given a partition k of d, the Specht module V_k is a finite dimensional vector space over C which admits a natural basis indexed by all standard tableaux of shape k with entries in {1, 2, ..., d}. It affords an irreducible representation of the symmetric group S_d, and conversely every irreducible representation of S_d is isomorphic to V_k for some partition k. Given two Specht modules V_k, V_t their tensor product representation is in general reducible, and hence it splits into a direct sum of irreducibles. This raises the problem of describing the S_d equivariant projection morphisms (alternately called S_d-homomorphisms) in terms of the standard tableaux basis. In this work we give explicit formulae describing this morphism in the following cases: k=(d-1, 1), (d-2, 1,1), (2, 1,... ,1). Finally, we present a conjecture formula for the q-morphism in the case k=(d-r, 1, ..., 1).

This thesis is devoted to a problem in the representation theory of the symmetric group over C (the field of the complex numbers). Let d be a positive integer, and let S_d denote the symmetric group on d letters. Given a partition k of d, the Specht module V_k is a finite dimensional vector space over C which admits a natural basis indexed by all standard tableaux of shape k with entries in {1, 2, ..., d}. It affords an irreducible representation of the symmetric group S_d, and conversely every irreducible representation of S_d is isomorphic to V_k for some partition k. Given two Specht modules V_k, V_t their tensor product representation is in general reducible, and hence it splits into a direct sum of irreducibles. This raises the problem of describing the S_d equivariant projection morphisms (alternately called S_d-homomorphisms) in terms of the standard tableaux basis. In this work we give explicit formulae describing this morphism in the following cases: k=(d-1, 1), (d-2, 1,1), (2, 1,... ,1). Finally, we present a conjecture formula for the q-morphism in the case k=(d-r, 1, ..., 1).

Thesis (Ph. D.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 233-241). Also available on the World Wide Web.

Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references (leaves 60-63).