MA5350 Combinatorics

Course Details

Introduction to Combinatorics, Pigeonhole principle, Permutations and Combinations, Generating functions and combinations, Binomial coefficients, Polya's theory (Burnside Lemma, Permutation and Symmetry Groups, Polya's Theorem), Principle of inclusion-exclusion and applications, Derangements, Permutations with forbidden positions, Recurrence relations, Catalan numbers, Bell numbers, Difference sequences and Stirling numbers, Partition numbers, Lattice paths and Schroder numbers, System of distinct representatives.

Course References:

Text Books:
1. R. A. Brualdi, Introductory Combinatorics, Pearson Modern Classics for Advanced Mathematics Series, 5th edition, 2019.

Reference Books:
1. P. J. Cameron, Combinatorics: Topics, Techniques, Algorithms, Cambridge University Press, 2001.
2. J. M. Harris, J. L. Hirst, M. J. Mossinghoff, Combinatorics and Graph Theory, Springer, 2nd edition, 2008.