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Computational and Constructive Design Theory

Computational and Constructive Design Theory
Author: W.D. Wallis
Publisher: Springer Science & Business Media
Total Pages: 371
Release: 2013-06-29
Genre: Mathematics
ISBN: 1475724977

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Over the last several years, there has been a significant increase in compu tational combinatorics. The most widely reported results were, of course, the proof of the Four Color Theorem and the proof that there is no projective plane of parameter 10. Although the computer was essential in both proofs, the only reason for this was the fact that life is short. The computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were just longer. Another important fact to notice is that both problems were theoretical, pure mathematical ones. The pursuit of the Four-Color Theorem has led to the development of whole branches of graph theory. The plane of parameter 10 is not an isolated case; its nonexistence is the first (and so far, the only) coun terexample to the conjecture that the Bruck-Chowla-Ryser conditions were necessary and sufficient for the existence of a symmetric balanced incomplete block design; the study of this problem has also led to a number of theoretical advances, including investigation of the relationship between codes and designs.


Designs 2002

Designs 2002
Author: W. D. Wallis
Publisher:
Total Pages: 386
Release: 2014-09-01
Genre:
ISBN: 9781461302469

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Algorithms in Combinatorial Design Theory

Algorithms in Combinatorial Design Theory
Author: C.J. Colbourn
Publisher: Elsevier
Total Pages: 347
Release: 1985-01-01
Genre: Mathematics
ISBN: 0080872255

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The scope of the volume includes all algorithmic and computational aspects of research on combinatorial designs. Algorithmic aspects include generation, isomorphism and analysis techniques - both heuristic methods used in practice, and the computational complexity of these operations. The scope within design theory includes all aspects of block designs, Latin squares and their variants, pairwise balanced designs and projective planes and related geometries.


Drifting by Intention

Drifting by Intention
Author: Peter Gall Krogh
Publisher: Springer Nature
Total Pages: 152
Release: 2020-03-11
Genre: Architecture
ISBN: 3030378969

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Constructive design research, is an exploratory endeavor building exemplars, arguments, and evidence. In this monograph, it is shown how acts of designing builds relevance and articulates knowledge in combination. Using design acts to build new knowledge, invite reframing of questions and new perceptions to build up. Respecting the emergence of new knowledge in the process invite change of cause and action. The authors' term for this change is drifting; designers drift; and they drift intentionally, knowing what they do. The book details how drifting is a methodic practice of its own and provides examples of how and where it happens. This volume explores how to do it effectively, and how it depends on the concept of knowledge. The authors identify four epistemic traditions in constructive design research. By introducing a Knowledge/Relevance model they clarify how design experiments create knowledge and what kinds of challenges and contributions designers face when drifting. Along the lines of experimental design work the authors identify five main ways in which constructive experiments drift. Only one of them borrows its practices from experimental science, others build on precedents including arts and craft practices. As the book reveals, constructive design research builds on a rich body of research that finds its origins in some of the most important intellectual movements of 20th century. This background further expands constructive design research from a scientific model towards a more welcoming understanding of research and knowledge. This monograph provides novel actionable models for steering and navigating processes of constructive design research. It helps skill the design researcher in participating in the general language games of research and helps the design researcher build research relations beyond the discipline.


Design Research Through Practice

Design Research Through Practice
Author: Ilpo Koskinen
Publisher: Elsevier
Total Pages: 223
Release: 2011-09-26
Genre: Computers
ISBN: 0123855020

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Human Computer Interaction (HCI), user interface design en usability.


Design Theory: Volume 1

Design Theory: Volume 1
Author: Thomas Beth
Publisher: Cambridge University Press
Total Pages: 730
Release: 1999-11-18
Genre: Mathematics
ISBN: 9780521444323

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This is the first volume of the second edition of the standard text on design theory.


Surveys in Combinatorics 2003

Surveys in Combinatorics 2003
Author: C. D. Wensley
Publisher: Cambridge University Press
Total Pages: 382
Release: 2003-07-24
Genre: Mathematics
ISBN: 9780521540124

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The British Combinatorial Conference is held every two years and is a key event for mathematicians worldwide working in combinatorics. In June 2003 the conference was held at the University of Wales, Bangor. The papers contained here are surveys contributed by the invited speakers and are of the high quality that befits the event. There is also a tribute to Bill Tutte who had a long-standing association with the BCC. The papers cover topics currently attracting significant research interest as well as some less traditional areas such as the combinatorics of protecting digital content. They will form an excellent resource for established researchers as well as graduate students who will find much here to inspire future work.


Designs 2002

Designs 2002
Author: W.D. Wallis
Publisher: Springer Science & Business Media
Total Pages: 370
Release: 2013-12-01
Genre: Mathematics
ISBN: 1461302455

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This volume is a sequel to our 1996 compilation, Computational and Constructive Design Theory. Again we concentrate on two closely re lated aspects of the study of combinatorial designs: design construction and computer-aided study of designs. There are at least three classes of constructive problems in design theory. The first type of problem is the construction of a specific design. This might arise because that one particular case is an exception to a general rule, the last remaining case of a problem, or the smallest unknown case. A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of "starter" designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding "starter" designs.


Recent Trends in Algebraic Combinatorics

Recent Trends in Algebraic Combinatorics
Author: Hélène Barcelo
Publisher: Springer
Total Pages: 362
Release: 2019-01-21
Genre: Mathematics
ISBN: 3030051412

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This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.


Semantic Techniques in Quantum Computation

Semantic Techniques in Quantum Computation
Author: Simon Gay
Publisher: Cambridge University Press
Total Pages: 497
Release: 2010
Genre: Computers
ISBN: 052151374X

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Explores quantum computation from the perspective of the branch of theoretical computer science known as semantics.