The Geometry of the Word Problem for Finitely Generated Groups (Advanced Courses in Mathematics

Book Description

The origins of the word problem are in group theory, decidability and complexity, but, through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry, including topics such as soap films, isoperimetry, coarse invariants and curvature.

The first part introduces van Kampen diagrams in Cayley graphs of finitely generated, infinite groups; it discusses the van Kampen lemma, the isoperimetric functions or Dehn functions, the theory of small cancellation groups and an introduction to hyperbolic groups.

One of the main tools in geometric group theory is the study of spaces, in particular geodesic spaces and manifolds, such that the groups act upon. The second part is thus dedicated to Dehn functions, negatively curved groups, in particular, CAT(0) groups, cubings and cubical complexes.

In the last part, filling functions are presented from geometric, algebraic and algorithmic points of view; it is discussed how filling functions interact, and applications to nilpotent groups, hyperbolic groups and asymptotic cones are given. Many examples and open problems are included.

Advances in Finite Geometries and Designs: Proceedings of the Third Isle of Thorns Conference 1990

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Advances in Finite Geometries and Designs: Proceedings of the Third Isle of Thorns Conference 1990

Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

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This volume comprises papers presented at the Third Isle of Thorns Conference on Finite Geometries and Designs. The papers explore the structure and associated incidence structures of Galois geometries, and their related automorphism groups. Among the main topics covered are generalized
quadrangles and n-gons, groups acting on geometries, linear spaces, partial geometries, diagram geometries, non-Desarguesian planes, strongly regular graphs, and designs. This timely collection of articles is expertly presented and will be of interest to research workers and postgraduates in
combinatorics, design theory, and finite geometries.

Handbook of Finite Translation Planes (Pure and Applied Mathematics)

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Handbook of Finite Translation Planes (Pure and Applied Mathematics)
Norman Johnson , Vikram Jha , and Mauro Biliotti
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Hardcover

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ASIN: 1584886056

Book Description

The Handbook of Finite Translation Planes provides a comprehensive listing of all translation planes derived from a fundamental construction technique, an explanation of the classes of translation planes using both descriptions and construction methods, and thorough sketches of the major relevant theorems. From the methods of André to coordinate and linear algebra, the book unifies the numerous diverse approaches for analyzing finite translation planes. It pays particular attention to the processes that are used to study translation planes, including ovoid and Klein quadric projection, multiple derivation, hyper-regulus replacement, subregular lifting, conical distortion, and Hermitian sequences. In addition, the book demonstrates how the collineation group can affect the structure of the plane and what information can be obtained by imposing group theoretic conditions on the plane. The authors also examine semifield and division ring planes and introduce the geometries of two-dimensional translation planes. As a compendium of examples, processes, construction techniques, and models, the Handbook of Finite Translation Planes equips readers with precise information for finding a particular plane. It presents the classification results for translation planes and the general outlines of their proofs, offers a full review of all recognized construction techniques for translation planes, and illustrates known examples.

An Algebraic Approach to Association Schemes (Lecture Notes in Mathematics)

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An Algebraic Approach to Association Schemes (Lecture Notes in Mathematics)
Paul-Hermann Zieschang
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

The primary object of the lecture notes is to develop a treatment of association schemes analogous to that which has been so successful in the theory of finite groups. The main chapters are decomposition theory, representation theory, and the theory of generators. Tits buildings come into play when the theory of generators is developed. Here, the buildings play the role which, in group theory, is played by the Coxeter groups. - The text is intended for students as well as for researchers in algebra, in particular in algebraic combinatorics.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 10th International Workshop, APPROX 2007, and 11th International ... (Lecture Notes in Computer Science)

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques: 10th International Workshop, APPROX 2007, and 11th International ... (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

This book constitutes the joint refereed proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2007 and the 11th International Workshop on Randomization and Computation, RANDOM 2007, held in Princeton, NJ, USA, in August 2007.

The 44 revised full papers presented were carefully reviewed and selected from 99 submissions. Topics of interest covered by the papers are design and analysis of approximation algorithms, hardness of approximation, small space and data streaming algorithms, sub-linear time algorithms, embeddings and metric space methods, mathematical programming methods, coloring and partitioning, cuts and connectivity, geometric problems, game theory and applications, network design and routing, packing and covering, scheduling, design and analysis of randomized algorithms, randomized complexity theory, pseudorandomness and derandomization, random combinatorial structures, random walks/Markov chains, expander graphs and randomness extractors, probabilistic proof systems, random projections and embeddings, error-correcting codes, average-case analysis, property testing, computational learning theory, and other applications of approximation and randomness.

Characters and Cyclotomic Fields in Finite Geometry

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Characters and Cyclotomic Fields in Finite Geometry
Bernhard Schmidt
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 354044243X

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This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13 <1 <4x10^(12). Finally, a conjecturally complete classification of all irreducible cyclic two-weight codes is obtained.

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Combinatorics of Finite Geometries
Lynn Margaret Batten
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521599938

Book Description

Combinatorics of Finite Geometries is an introductory text on the combinatorial theory of finite geometry. Assuming only a basic knowledge of set theory and analysis, it provides a thorough review of the topic and leads the student to results at the frontiers of research. This book begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes. Later, it addresses polar spaces, partial geometries, and generalized quadrangles. The revised edition contains an entirely new chapter on blocking sets in linear spaces, which highlights some of the most important applications of blocking sets--from the initial game-theoretic setting to their very recent use in cryptography. Extensive exercises at the end of each chapter insure the usefulness of this book for senior undergraduate and beginning graduate students.

Commutative Algebra: Proceedings of a Workshop Held in Salvador, Brazil, Aug. 8-17, 1988 (Lecture Notes in Mathematics)

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Commutative Algebra: Proceedings of a Workshop Held in Salvador, Brazil, Aug. 8-17, 1988 (Lecture Notes in Mathematics)
Brazil) Workshop in Commutative Algebra (1988 Salvador
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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Book Description

The central theme of this volume is commutative algebra, with emphasis on special graded algebras, which are increasingly of interest in problems of algebraic geometry, combinatorics and computer algebra. Most of the papers have partly survey character, but are research-oriented, aiming at classification and structural results.

Finite Fields and Applications: Proceedings of The Fifth International Conference on Finite Fields and Applications Fq5, held at the University of Augsburg, Germany, August 2-6, 1999

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Finite Fields and Applications: Proceedings of The Fifth International Conference on Finite Fields and Applications Fq5, held at the University of Augsburg, Germany, August 2-6, 1999

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540411097

Book Description

The Fifth International Conference on Finite Fields and Applications Fq5 held at the University of Augsburg, Germany, from August 2-6, 1999 continued a series of biennial international conferences on finite fields. The proceedings document the steadily increasing interest in this topic. Finite fields have an inherently fascinating structure and are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields. This interplay has always been a dominant theme in Fq conferences and was very much in evidence at Fq5. The proceedings reflect this, and offer an up-to-date collection of surveys and original research articles by leading experts in the area.

Finite Geometries (Developments in Mathematics)

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Finite Geometries (Developments in Mathematics)

Manufacturer: Springer
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Binding: Hardcover

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Book Description

This is a graduate-level book aimed at experienced researchers as well as beginning graduate students in finite geometry, incidence geometry, design theory, coding theory and combinatorics. The 21 articles arise from the Fourth Isle of Thorns Conference on Finite Geometries, held in July 2000. The book contains new high-level results at the forefront of the field as well as authoritative surveys. The articles are written so that beginning graduate students can appreciate them.
Among the surveys by the invited speakers are P.J. Cameron `Fixed Points and cycles', C.E. Praeger `Implications of line-transitivity for designs', B. Schmidt, `Exponent bounds', which explains recent results on difference sets, and several papers with H. Van Maideghem as co-author on generalized polygons.
The editors also contribute: A. Blokhuis, D. Jungnickel, and B. Schmidt `On a class of symmetric divisible designs which are almost projective planes', and D. Luyckx and J.A. Thas discuss the geometry of the quadric in six dimensions. There is also a lengthy and complete survey by J.W.P. Hirschfeld and L. Storme `The packing problem in statistics, coding theory and finite projective spaces: update 2001'.
Audience: Researchers as well as beginning graduate students in the areas of finite geometry, incidence geometry, design theory, coding theory and combinatorics will appreciate the surveys and original papers by leaders in these fields.

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Wilkie Collins, whom many consider the originator of the modern detective story in novels such as The Moonstone and The Woman in White, wrote this novel when he was 19 and fired up with dreams of far-off places and heroic derring-do. Set in Polynesia in the days before European colonization, Iolani is filled with beautiful and long-suffering dusky-skinned women (with European features and heaving bosoms), wicked high priests, and even wild-eyed wild men from the forest. There are pitched battles between tribes, horrid pagan rituals, and plenty of damsels in distress, all played out against an exotic, tropical background of white beaches and swaying palm trees. In short, this is exactly the kind of overwrought romance one might expect from an imaginative young man with literary longings. Iolani, the title character, is the villain of the piece; shortly after his wife, Idia, gives birth to a son, he decides that in keeping with the religious practices of their tribe, the child must be put to death. Idia objects and ends up fleeing with the newborn and a beautiful young friend to seek protection from another tribe. Much melodrama ensues as Collins tries to fit the sensational conventions of the gothic potboiler popularized by writers such as Horace Walpole and Ann Radcliffe into a South Seas setting.

Never published during its author's lifetime, this is a novel that probably only Collins scholars could love. But even in the overheated prose and patently second- and third-hand descriptions of exotic locales, one can detect the seeds of his later, more successful works. Certainly Collins's fascination with sensational plots is evident here, but so is his radical (for the time) depiction of strong and unconventional women. Read Iolani for its historical interest; then take a look at The Moonstone to see how well Wilkie Collins grew up. --Margaret Prior

Book Description

"It is not an exaggeration to claim that the resurfacing of Iolani, the first stab at fiction by a major Victorian novelist, is a literary event of genuine importance."--Glenn Horowitz, Bookseller, New York.

Written 150 years ago, never published, and presumed lost for nearly a century, Wilkie Collins's earliest novel now appears in print for the first time. Iolani is a sensational romance--a tale of terror and suspense, bravery and betrayal, set against the lush backdrop of Tahiti. The book's complicated history is worthy of a writer famous for intricate plots hinging on long-kept secrets. Collins wrote the book as a young man in the early 1840s, twenty years before The Moonstone and The Woman in White made his name among Victorian novelists. He failed to find a publisher for the work, shelved the manuscript for years, and eventually gave it to an acquaintance. It disappeared into the hands of private collectors and remained there--acquiring mythical status as a lost novel--from the turn of the century until its sudden appearance on the rare book market in New York in 1991. This first edition appears with the permission of the new owners, who keep the mystery alive by remaining anonymous.

The novel is set in Tahiti prior to European contact. It tells the story of the diabolical high priest, Iolani , and the heroic young woman, Idia, who bears his child. Determined to defy the Tahitian custom of killing firstborn children, Idia and her friend Aimata flee with the baby and take refuge among Iolani`s enemies. The vengeful priest pursues them, setting into motion a plot that features civil war, sorcery, sacrificial rites, wild madmen, treachery, and love. Collins explores themes that he would return to again and again in his career: oppression by sinister, patriarchal figures; the bravery of forceful, unorthodox women; the psychology of the criminal mind; the hypocrisy of moralists; and Victorian ideas of the exotic. As Ira Nadel shows in his introduction, the novel casts new light on Collins's development as a writer and on the creation of his later masterpieces. A sample page from the manuscript appears as the frontispiece to this edition. The publication of Iolani is a major literary event: a century and half late, Wilkie Collins makes his literary debut as he originally intended it.

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The stumbling first work of a promising young author!.......2005-10-30

Now revered as a giant of classic English literature, Wilkie Collins clearly learned from the missteps of his first efforts. For this, we can be grateful! But it must be admitted that Collins' first attempt at a novel has an overwrought hoary plot much more suited to a breathless Harlequin romance or a melodramatic soap opera set in the South Pacific.

Idia, abandoned as a young girl and barely past childhood herself, finds the child, Aimata, forsaken by her natural guardians, and assumes the responsibility for care and upbringing. Although Aimata has always felt some deep misgivings about him, Idia is swept away by Iolani, the high priest of Oro, and bears his son. When Iolani attempts to enforce the Tahitian custom of slaying his first born, Idia, Aimata and the child flee for their lives seeking refuge in the village of rival chieftain, Mahini. Falling in love with the girl child, Aimata, Mahini sees the events as an opportunity to achieve his matrimonial as well as his leadership ambitions and provokes an all out tribal war with Iolani and his brother, the king of Tahiti. Sorcery, sacrifice, bloodshed, treachery and mayhem ensue.

While the plot and the milieu are so far removed from what we will enjoy in Collins' later work as to be sadly laughable, there are germs of ideas and spots of beauty that shine through and clearly persist into the much more polished output for which he became so famous - the psychology of female victim and male villain; assertive, independent and aggressive heroines; the use of his own voice as a narrator to insert explanatory information from time to time; courage and determination in the face of danger and extremity; lush, descriptive passages -

"The thunder still sounded its hollow retreat in the distance, and the rain drops still pattered faintly on the torn, dripping leaves of the forest. The waters of the lake, had changed in the night to a monotonous dun colour and still heaved wearily about, though the violence of the tempest was over and past. The tops of the mountains were hidden in deep mists and the thick, black clouds of a few hours since, had amalgamated into great masses of a grey hue, cold and indistinct to look upon, yet promising, in the eastern heaven, a bright and beautiful day."

and short gems of philosophy that cannot fail to provoke thought and discussion -

"While liberty frees the body, captivity loosens the soul. It is when the body is in bonds, that the spirit most experiences its perilous privilege of freedom."

If you're a confirmed Collins fan, you're sure to enjoy Iolani and recognize it for what it is - the stumbling first work of a promising young author. If you have yet to read anything by Collins, for goodness' sake, be sure you DON'T start here! Pick up A Woman in White or The Moonstone, and move on to Blind Love, Armadale and The Law and the Lady. By then you'll be a confirmed fan and you can come back to this one.

Paul Weiss

Iolani or Tahiti As it Was A Romance.......2000-05-08

This book was very difficult to understand because it is written in difficult english with many big words. I didnt understand what it meant until i read reviews amd summaries of it. I wouldnt recomend it unless you want to be constantly looking up words in the dictionary.

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Ioláni o Tahití tal como era
Wilkie Collins
Manufacturer: Valdemar
ProductGroup: Book
Binding: Hardcover

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IOLANI; OR TAHITI AS IT WAS: A ROMANCE
Wilkie Collins
Manufacturer: Horowitz New York, NY none given
ProductGroup: Book
Binding: Paperback

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