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Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups

2009-10-08 Mathematics
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Release : 2009-10-08
Genre : Mathematics
Kind : eBook
Book Rating : 903/5 ( reviews)

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Book Synopsis Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups by : Drew Armstrong

Download or read book Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups written by Drew Armstrong. This book was released on 2009-10-08. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.

Combinatorics of Set Partitions

2012-07-27 Computers
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Release : 2012-07-27
Genre : Computers
Kind : eBook
Book Rating : 342/5 ( reviews)

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Book Synopsis Combinatorics of Set Partitions by : Toufik Mansour

Download or read book Combinatorics of Set Partitions written by Toufik Mansour. This book was released on 2012-07-27. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on a very active area of mathematical research in the last decade, Combinatorics of Set Partitions presents methods used in the combinatorics of pattern avoidance and pattern enumeration in set partitions. Designed for students and researchers in discrete mathematics, the book is a one-stop reference on the results and research activities

Advances in Combinatorics

2013-08-04 Mathematics
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Release : 2013-08-04
Genre : Mathematics
Kind : eBook
Book Rating : 798/5 ( reviews)

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Book Synopsis Advances in Combinatorics by : Ilias S. Kotsireas

Download or read book Advances in Combinatorics written by Ilias S. Kotsireas. This book was released on 2013-08-04. Available in PDF, EPUB and Kindle. Book excerpt: This volume, as Andrew M. Odlzyko writes in the foreword, “commemorates and celebrates the life and achievements of an extraordinary person.” Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute. Professor Wilf was an award-winning teacher, who was supportive of women mathematicians, and who had an unusually high proportion of women among his PhD candidates. He was Editor-in-chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher, driven by his desire to know and explain the inner workings of the mathematical world. The book collects high-quality, refereed research contributions by some of Professor Wilf’s colleagues, students, and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011, W80), held May 26-29, 2011 at Wilfrid Laurier University, Waterloo, Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf’s contributions to mathematics and mathematical life.

Recent Trends in Algebraic Combinatorics

2019-01-21 Mathematics
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Release : 2019-01-21
Genre : Mathematics
Kind : eBook
Book Rating : 412/5 ( reviews)

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Book Synopsis Recent Trends in Algebraic Combinatorics by : Hélène Barcelo

Download or read book Recent Trends in Algebraic Combinatorics written by Hélène Barcelo. This book was released on 2019-01-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Generalised Jacobson-Morosov Theorem

2010-08-06 Mathematics
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Release : 2010-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 95X/5 ( reviews)

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Book Synopsis The Generalised Jacobson-Morosov Theorem by : Peter O'Sullivan

Download or read book The Generalised Jacobson-Morosov Theorem written by Peter O'Sullivan. This book was released on 2010-08-06. Available in PDF, EPUB and Kindle. Book excerpt: The author considers homomorphisms $H \to K$ from an affine group scheme $H$ over a field $k$ of characteristic zero to a proreductive group $K$. Using a general categorical splitting theorem, Andre and Kahn proved that for every $H$ there exists such a homomorphism which is universal up to conjugacy. The author gives a purely group-theoretic proof of this result. The classical Jacobson-Morosov theorem is the particular case where $H$ is the additive group over $k$. As well as universal homomorphisms, the author considers more generally homomorphisms $H \to K$ which are minimal, in the sense that $H \to K$ factors through no proper proreductive subgroup of $K$. For fixed $H$, it is shown that the minimal $H \to K$ with $K$ reductive are parametrised by a scheme locally of finite type over $k$.

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