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Combinatorics

Combinatorics is a topic in math within the broader area of discrete mathematics. In essence, it deals with methods for counting discrete structures and techniques for arranging objects according to stated rules. As such, it will involve basic ideas like permutations and combinations. Normally, however, full semester courses in combinatorics are approached at advanced levels with topics that can become quite sophisticated.

A college-level course in combinatorics may involve study in the following areas:

  • Numbers and counting
  • Subsets, partitions, permutations
  • Recurrence relations and generating functions
  • The principle of inclusion and exclusion
  • Latin squares and SDRs
  • Extremal set theory
  • Steiner triple theory
  • Finite geometry
  • Ramsey's theorem
  • Graphs
  • Posets, lattices and matroids
  • More on partitions and permutations
  • Automorphism groups and permutation groups
  • Enumeration under group action
  • Designs
  • Error-correcting codes
  • Graph colorings
  • The infinite

For those counting enthusiasts, a visit to Peter Cameron's home page should prove interesting, although his official academic site can be found at the University of London. To stay up to date with combinatorics, students should read the European Journal of Combinatorics.

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