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Combinatorial Properties of Shifted Complexes

2003
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Release : 2003
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Book Synopsis Combinatorial Properties of Shifted Complexes by : Caroline Jane Klivans

Download or read book Combinatorial Properties of Shifted Complexes written by Caroline Jane Klivans. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study the class of shifted simplicial complexes. A simplicial complex on n nodes is shifted if there exists a labelling of the nodes by 1 through n such that for any face, replacing any node of the face with a node of smaller label results in a collection which is also a face. A primary motivation for considering shifted complexes is a procedure called shifting. Shifting associates a shifted complex to any simplicial complex in a way which preserves meaningful information, while simplifying the structure of the complex. For example, shifting preserves the f-vector of a complex but always reduces the topology to a wedge of spheres. Shifting has proved to be a successful tool for answering questions regarding f-vectors. While most of the previous results on shifted complexes are algebraic or topological in nature, we explore the combinatorics of shifted complexes. We give intrinsic characterization theorems for shifted complexes and shifted matroid complexes. In addition, we show results on the enumeration of shifted complexes and connections to various combinatorial structures.

Topological and Combinatorial Properties of Random Simplicial Complexes

2007
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Release : 2007
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Book Synopsis Topological and Combinatorial Properties of Random Simplicial Complexes by : Nathan Simon Wallach

Download or read book Topological and Combinatorial Properties of Random Simplicial Complexes written by Nathan Simon Wallach. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Trends in Combinatorics

2016-04-12 Mathematics
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Release : 2016-04-12
Genre : Mathematics
Kind : eBook
Book Rating : 989/5 ( reviews)

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Book Synopsis Recent Trends in Combinatorics by : Andrew Beveridge

Download or read book Recent Trends in Combinatorics written by Andrew Beveridge. This book was released on 2016-04-12. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus. Leading experts have written surveys of research problems, making state of the art results more conveniently and widely available. The three-part structure of the volume reflects the three workshops held during Fall 2014. In the first part, topics on extremal and probabilistic combinatorics are presented; part two focuses on additive and analytic combinatorics; and part three presents topics in geometric and enumerative combinatorics. This book will be of use to those who research combinatorics directly or apply combinatorial methods to other fields.

Simplicial Complexes of Graphs

2007-11-15 Mathematics
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Release : 2007-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 585/5 ( reviews)

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Book Synopsis Simplicial Complexes of Graphs by : Jakob Jonsson

Download or read book Simplicial Complexes of Graphs written by Jakob Jonsson. This book was released on 2007-11-15. Available in PDF, EPUB and Kindle. Book excerpt: A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up naturally in many different areas of mathematics. Identifying each graph with its edge set, one may view a graph complex as a simplicial complex and hence interpret it as a geometric object. This volume examines topological properties of graph complexes, focusing on homotopy type and homology. Many of the proofs are based on Robin Forman's discrete version of Morse theory.

Combinatorial Methods in Topology and Algebra

2015-10-31 Mathematics
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Release : 2015-10-31
Genre : Mathematics
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Book Rating : 557/5 ( reviews)

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Book Synopsis Combinatorial Methods in Topology and Algebra by : Bruno Benedetti

Download or read book Combinatorial Methods in Topology and Algebra written by Bruno Benedetti. This book was released on 2015-10-31. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.

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