An introduction to the basic notions and techniques in enumerative combinatorics. Topics include generating functions, principle of inclusion and exclusion, bijections, recurrence relations, partially ordered sets, the Möbius function and Möbius algebra, Lagrange inversion formula, the exponential formula and tree enumeration.
The material has applications to active areas of research including polytopal theory, hyperplane arrangements, computational commutative algebra, representation theory and symmetric functions.
Prerequisite: A graduate course in linear algebra or permission of instructor.
Richard P. Stanley, Enumerative combinatorics. Vol. 2. Cambridge Studies in Advanced Mathematics, 62. Cambridge University Press, Cambridge, 1999.
Herb Wilf, Generatingfunctionology, Second edition, Academic Press, Inc., Boston, MA, 1994.