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COMBINATORICS

Outline:

  1. Counting, permutations, and partitions
  2. Recurrence relations and generating functions
  3. Principle of inclusion and exclusion, and extremal set theory,
  4. Posets, lattices, and set systems
  5. Graphs, digraphs, Graph colorings, convexity, and eccentricity

Objective:

In the course, we will introduce basic counting methods and important theorems in combinatorial theory, discuss the relations between combinatorial theory and graph theory, and study some related research problems.

Textbook:

  1. P. J. Cameron, Combinatorics: Topics, techniques, Algorithm, Cambridge, 1998.
  2. B. Bolloás, Combinatorics, Cambridge , 1986.
  3. J. H. von Lint and R. M. Wilson, A course in Combinatorics, Cambridge, 1992.
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