Thesis (PhD)--Macquarie University, Division of Humanities, Department of English, 2004. / Bibliography: leaves 270-277. / Introduction -- George MacDonald's religious heritage -- George MacDonald's philosophical and literary roots -- Of friends and teachers -- Conversion studies and critical application -- Children on the path -- Waking from slumber -- Courageous stances -- Toppled pride -- Broken vessels -- Implications of MacDonald's conversion depictions. / Victorian author George MacDonald is best remembered for his writing in the genres of fairy tale and fantasy. MacDonald was, however, most popular during his own time as a writer of realistic adult fiction. He was widely read but critically dismissed as a writer whose works were both didactic and predictable in plot. MacDonald was primarily a teacher who used the novel as a means to convey to readers his Christian message of hope and transformation. -- This thesis begins with a study of those individuals and ideas that influenced MacDonald's thoughts and beliefs. The second part of this thesis is an overview of studies of spiritual conversion, with particular emphasis on the works of V. Bailey Gillespie, Lewis Rambo, John Lofland, and Norman Skonovd. Their works in the field of conversion studies include several schemata which are helpful in explaining specific depictions of conversion within MacDonald's adult fiction. -- The remainder of the thesis focuses on MacDonald's portrayals of characters who experience conversion in his novels. They are placed into the following categories: Children on the Path; Waking from Slumber; Courageous Stances; Toppled Pride; and Broken Vessels. The experiences of the characters are thoroughly examined and justification is offered for their inclusions in their respective categories. -- This study counters the criticism levelled at MacDonald during his own time that he was caught in repetitive plots for lack of skill or inspiration. My findings suggest that MacDonald's depictions show a deep as well as wide understanding of the process of conversion, an understanding which seems to have encompassed a broader understanding than those of most of the religious writers of his own day. I suggest that his focus was on his message rather than his art. Therefore, his adult realistic fiction constitutes a very substantial literary achievement and offers contemporary readers and writers a benchmark against which to measure both their own understandings of conversion and their own expressions of it. / Mode of access: World Wide Web. / 277 leaves

Thesis (Ph.D.) - University of St Andrews, May 2008. / Restricted until 9th May 2013, during which time access is available with the consent of the Head of School.

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The original Macdonald polynomials P_μ form a basis for the vector space of symmetric functions which specializes to several of the common bases such as the monomial, Schur, and elementary bases. There are a number of different types of Macdonald polynomials obtained from the original P_μ through a combination of algebraic and plethystic transformations one of which is the modified Macdonald polynomial H̃_μ. In this dissertation, we study a certain specialization F̃_μ(q,t) which is the coefficient of x₁x₂…x_N in H̃_μ and also the Hilbert series of the Garsia-Haiman module M_μ. Haglund found a combinatorial formula expressing F̃_μ as a sum of n! objects weighted by two statistics. Using this formula we prove a q,t-analogue of the hook-length formula for hook shapes. We establish several new combinatorial operations on the fillings which generate F̃_μ. These operations are used to prove a series of recursions and divisibility properties for F̃_μ. / Ph. D.

Nonsymmetric Macdonald polynomials can be symmetrized in all their variables to obtain the (symmetric) Macdonald polynomials. We generalize this process, symmetrizing the nonsymmetric Macdonald polynomials in only the first k out of n variables. The resulting partially-symmetric Macdonald polynomials interpolate between the symmetric and nonsymmetric types. We begin developing theory for these partially-symmetric polynomials, and prove results including their stability, an integral form, and a Pieri-like formula for their multiplication with certain elementary symmetric functions. / Doctor of Philosophy / There are two well-understood types of polynomials known as the nonsymmetric Macdonald polynomials and symmetric Macdonald polynomials. We define a new form of Macdonald polynomials, which we call partially-symmetric, that are somewhere between the symmetric and nonsymmetric versions. We examine properties of these new partially-symmetric polynomials, including what happens when adding additional symmetric variables, how to multiply them by a constant to clear out denominators in their coefficients, and what happens when multiplying them by another symmetric polynomial.

Thesis (M.A.)--Université de Sherbrooke, 1999. / Includes bibliographical references.

La théorie sur les polynômes de Macdonald a fait l'objet d'une quantité importante de recherches au cours des dernières années. Définis originellement par Macdonald comme une généralisation de quelques-unes des bases les plus importantes de l'anneau des fonctions symétriques, ces polynômes ont des applications dans des domaines tels que la théorie des représentations des groupes quantiques et physique des particules. Ce travail présente quelques-uns des résultats combinatoires les plus importants entourant ces polynômes, en mettant particulièrement l'accent sur la formule combinatoire prouvée récemment par Haglund, Haiman et Loehr pour les polynômes de Macdonald. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Polynômes de Macdonald, Fonctions symétriques, Combinatoire algébrique, Combinatoire énumérative, Théorie des représentations, Géométrie algébrique.

L'introduction des polynômes de Macdonald (Macdonald, 1988) comme des vecteurs propres associés à certains opérateurs reliés à la physique et comme une généralisation de quelques-unes des bases les plus importantes de l'anneau des fonctions symétriques, a donné lieu à un nombre remarquable de résultats dans divers domaines de l'algèbre, la combinatoire et la géométrie algébrique, entre autres. Ce travail présente un des liens entre la théorie des fonctions symétriques et la théorie des représentations des groupes, donné par les polynômes de Macdonald et les modules de Garsia-Haiman. ______________________________________________________________________________ MOTS-CLÉS DE L’AUTEUR : Combinatoire algébrique, Combinatoire énumérative, Fonctions symétriques, Modules de Garsia-Haiman, Polynômes de Macdonald, Théorie des représentations.

Cette thèse est consacrée au problème de combinatoire algébrique appelée conjecture n!. <br /><br />Plus explicitement, on étudie la structure de certains espaces notés M_mu et indexés par les partitions mu de l'entier n. Chaque espace M_mu est le cône de dérivation d'un polynôme Delta_mu, généralisant en deux alphabets le déterminant de Vandermonde. Le coeur de ce travail, motivé par l'interprétation de certains polynômes de Macdonald en termes de multiplicité des représentations irréductibles du S_n-module M_mu, est la conjecture n!, énoncée en 1991 par A. Garsia et M. Haiman et récemment prouvée par ce dernier. <br /><br />On s'intéresse ici tout d'abord à l'explicitation de bases monomiales des espaces M_mu. Cette approche est très liée à l'étude de l'idéal annulateur de Delta_mu et nous conduit à introduire certains opérateurs de dérivation, dits opérateurs de sauts. On obtient une base monomiale explicite et une description de l'idéal annulateur pour les partitions en équerres, et pour le sous-espace en un alphabet M_mu(X) avec une partition mu quelconque. <br /><br />Les opérateurs de sauts se révèlent cruciaux pour l'introduction et l'étude de généralisations de la conjecture n!. Dans le cas des partitions trouées (approche récursive de la conjecture n!), l'obtention d'une base explicite du sous-espace en un alphabet permet de traiter une spécialisation de la fondamentale récurrence à quatre termes. Dans le cas des diagrammes à plusieurs trous, l'introduction de sommes de cônes de dérivation permet d'énoncer une conjecture généralisant la conjecture n!, supportée par l'obtention d'une borne supérieure et la structure du sous-espace en un alphabet.