Sharad S. Sane

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.

Design theory is a branch of combinatorics with applications in number theory, coding theory and geometry. In this, the first book on the subject, the authors discuss the generalization of results and applications to quasi-symmetric designs. The coverage is comprehensive and will be useful for researchers and graduate students. An attractive feature is the discussion of unsolved problems.