Course Description

MATH 8005. Enumerative Combinatorics I

Course Code MATE 8005
Course Title Enumerative Combinatorics I
Credits 3
Hours 3 per week
Prerequisites MATH 6150, MATH 6201, MATH 8001
Description Review of elementary combinatorics. Outline of the main problems and approaches of enumerative combinatorics. Enumerating trees. Matrix-tree theorem. Coding of trees. Counting Euler cycles in a digraph. Counting and listing of non-isomorphic trees of different types. Generating function method in enumerative combinatorics. Enumerating graphs of different types. Pólyas’s counting theory of non-isomorphic objects. Enumerating non-isomorphic graphs of different types. Principle of inclusion and exclusion. Lattices, their Möbius functions and Möbius algebras. Asymptotic results in enumerative combinatorics.
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