Combinatorics

Code: MA510 | L-T-P-C: 3-0-0-6

Counting principles, multinomial theorem, set partitions and Striling numbers of the second kind, permutations and Stirling numbers of the first kind, number partitions, Lattice paths, Gaussian coefficients, Aztec diamonds, formal series, infinite sums and products, infinite matrices, inversion of sequences, probability generating functions, generating functions, evaluating sums, the exponential formula, more on number partitions and infinite products, Ramanujan's formula, hypergeometric sums, summation by elimination, infinite sums and closed forms, recurrence for hypergeometric sums, hypergeometric series, Sieve methods, inclusion-exclusion, Mobius inversion, involution principle, Gessel-Viennot lemma, Tutte mtrix-tree theorem, enumeration and patterns, Polya-Redfield theorem, cycle index, symmetries on N and R, polyominoes

Texts:

1. M. Aigner. A Course in Enumeration. Springer, GTM, 2007.

References:

1. C. Berge. Principles of Combinatorics. Academic Press,1971.
2. J. Riordan. Introduction to Combinatorial Analysis. Dover,2002.
3. M. Bona. Introduction to Enumerative Combinatorics. Tata McGraw Hill, 2007.