Texts and Readings in Mathematics

This is a basic text on combinatorics that deals with all the three aspects of the discipline: tricks, techniques and theory, and attempts to blend them.

The book has several distinctive features. Probability and random variables with their interconnections to permutations are discussed. The theme of parity has been specially included and it covers applications ranging from solving the Nim game to the quadratic reciprocity law. Chapters related to geometry include triangulations and Sperner's theorem, classification of regular polytopes, tilings and an introduction to the Eulcidean Ramsey theory. Material on group actions covers Sylow theory, automorphism groups and a classification of finite subgroups of orthogonal groups.

All chapters have a large number of exercises with varying degrees of difficulty, ranging from material suitable for Mathematical Olympiads to research.
1 Basic counting
2 Listing combinatorial objects
3 Permutations
4 The inclusion-exclusion principle
5 Basic probability
6 Random variables
7 Parity
8 Pigeonhole principle
9 Some geometry
10 Advanced counting numbers
11 Recurrence relations
12 Generating functions
13 Partition theory of integers
14 Group action on a set
15 Polya theory of enumeration
16 Systems of distinct representatives
References
Index