Books on Combinatorics
Singular Loci of Schubert Varieties
Sara Billey and V. Lakshmibai
Birkhäuser Boston  September 29, 2000

"Singular Loci of Schubert Varieties" is a unique work at the crossroads of representation theory, algebraic geometry, and combinatorics. Over the past 20 years, many research articles have been written on the subject in notable journals. In this work, Billey and Lakshmibai have recreated and restructured the various theories and approaches of those articles and present a clearer understanding of this important subdiscipline of Schubert varieties – namely singular loci. The main focus, therefore, is on the computations for the singular loci of Schubert varieties and corresponding tangent spaces. The methods used include standard monomial theory, the nil Hecke ring, and Kazhdan-Lusztig theory. New results are presented with sufficient examples to emphasize key points. A comprehensive bibliography, index, and tables – the latter not to be found elsewhere in the mathematics literature – round out this concise work. After a good introduction giving background material, the topics are presented in a systematic fashion to engage a wide readership of researchers and graduate students.

Special Functions, An Introduction to the Classical Functions of Mathematical Physics
Nico M. Temme
Wiley-Interscience  January 1, 2001

This book gives an introduction to the classical, well-known special functions which play a role in mathematical physics, especially in boundary value problems. Calculus and complex function theory form the basis of the book and numerous formulas are given. Particular attention is given to asymptomatic and numerical aspects of special functions, with numerous references to recent literature provided.

Spectral Graph Theory
Fan R. K. Chung
American Mathematical Society  May 1997

Beautifully written and elegantly presented, this book is based on 10 lectures given at the CBMS workshop on spectral graph theory in June 1994 at Fresno State University. Chung's well-written exposition can be likened to a conversation with a good teacher--one who not only gives you the facts, but tells you what is really going on, why it is worth doing, and how it is related to familiar ideas in other areas. The monograph is accessible to the nonexpert who is interested in reading about this evolving area of mathematics.

Subgroup lattices and symmetric functions
Lynne M. Butler
AMS  1994

Substitutions in Dynamics, Arithmetics and Combinatorics
N. Pytheas Fogg, Valerie Berthé, Sebastien Ferenczi, Christian Mauduit, Anne Siegel
Springer  November 11, 2002

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure.The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Symbolic Integration 1
Manuel Bronstein
Springer  January 21, 1997

This book, the first volume in the new series Algorithms and Computation in Mathematics, is bound to become the standard reference for symbolic integration. The author is the leading expert on this topic and his book is the first book to treat it comprehensively and in detail including new results. Many algorithms are given in pseudocode and, hence, can be implemented. The book addresses mathematicians and computer scientists who are interested in symbolic computation, developers and programmers of computer algebra systems and users of symbolic integration methods. It will also serve as a textbook to be used for lecture courses on symbolic integration.

Symmetric Functions 2001: Surveys of Developments and Perspectives
Sergey Fomin
Springer  April 16, 2003

This book surveys recent developments and outlines research prospects in various fields, the fundamental questions of which can be stated in the language of symmetric functions. Interdisciplinary interconnections are emphasized.

Symmetric Functions and Combinatorial Operators on Polynomials
Alain Lascoux
American Mathematical Society  November 2003

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