Books on Combinatorics
Advanced Linear Algebra
Steven Roman
Springer  November 19, 2010

This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

Advances in Algebra And Combinatorics
K. P. Shum, E. Zelmanov, Jiping Zhang, Shangzhi Li
World Scientific  June 2008

This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Algebraic and Geometric Combinatorics
Christos A. Athanasiadis et al.
Amer Mathematical Society  May 2007

This volume contains original research and survey articles stemming from the Euroconference ``Algebraic and Geometric Combinatorics''. The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

Algebraic Combinatorics
P.Orlik, V. Welker, G. Floystad
Springer  April 20, 2001

Algebraic graph theory is a combination of two strands. The first is the study of algebraic objects associated with graphs. The second is the use of tools from algebra to derive properties of graphs. The authors' goal has been to present and illustrate the main tools and ideas of algebraic graph theory, with an emphasis on current rather than classical topics. While placing a strong emphasis on concrete examples, the authors tried to keep the treatment self-contained.

Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota
Henry H. Crapo, Gian-Carlo Rota, Domenico Senato
Springer-Verlag Italia Srl  November 2000

This volume consists of a selection of surveys and research papers on algebraic combinatorics and theoretical computer science given during the 6th Italian Congress on Algebraic Combinatorics held in October 1999 in Maratea (Italy)

Algebraic Combinatorics and Quantum Groups
Naihuan Jing
World Scientific Publishing Company  September 2003

Algebraic combinatorics has evolved into one of the most active areas of mathematics during the last several decades. Its recent developments have become more interactive with not only its traditional field representation theory but also algebraic geometry, harmonic analysis and mathematical physics.

Algebraic Combinatorics on Words
M. Lothaire
Cambridge University Press  April 2002

Algebraic Combinatorics: Walks, Trees, Tableaux, and More
Richard P. Stanley
Springer, New York  June, 2013

The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and rudiments of group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, de Bruijn sequences, the Erd?s-Moser conjecture, electrical networks, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees.

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