Enumerative Combinatorics: Volume 1
by Richard P. Stanley
Publisher: MIT 2011
Number of pages: 725
The standard guide to the topic for students and experts alike. The material in Volume 1 was chosen to cover those parts of enumerative combinatorics of greatest applicability and with the most important connections with other areas of mathematics.
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by Dainis Zeps - Latvian University
Contents: Permutations; Combinatorial maps; The correspondence between combinatorial maps and graphs on surfaces; Map's mirror reflection and dual map; Multiplication of combinatorial maps; Normalized combinatorial maps; Geometrical interpretation...
by Louis J. Billera, at al. - Cambridge University Press
The rich combinatorial problems arising from the study of various algebraic structures are the subject of the book. It will present the state of the art to graduate students and researchers in combinatorics as well as algebra, geometry, and topology.
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Matroids were introduced in 1935 as an abstract generalization of graphs and matrices. Matroid decomposition covers the area of the theory dealing with decomposition and composition of matroids. The exposition is clear and simple.
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The main goal of this survey is to state clearly and concisely some of the most useful tools in algebraic and geometric enumeration, and to give many examples that quickly and concretely illustrate how to put these tools to use.