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This is a text with more than enough material for a one-semester introduction to combinatorics. The original target audience was primarily computer science majors, but the topics included make it suitable for a variety of different students. Topics include

  • Basic enumeration: strings, sets, binomial coefficients
  • Recursion and mathematical induction
  • Graph theory
  • Partially ordered sets
  • Additional enumeration techniques: inclusion-exclusion, generating functions, recurrence relations, and Polya theory.
  • Graph algorithms: minimum weight spanning trees, Dijkstra's algorithm, network flows

This text is open source and available under a Creative Commons license. To access the free HTML and PDF versions of the text,

About the Author

Mitchel T. Keller is an assistant professor in the Department of Mathematics at Washington and Lee University, a small liberal arts college in Lexington, Virginia. He holds a B.S. in mathematics from North Dakota State University and a Ph.D. in mathematics from the Georgia Institute of Technology. Mitchís research interests are in the combinatorics of partially ordered sets, online algorithms and combinatorial approaches to Stanley depth of monomial ideals. He likes to travel, bake and take photographs. Mitch is also the Managing Director of the Mathematics Genealogy Project.

William T. Trotter is a professor in the School of Mathematics at the Georgia Institute of Technology in Atlanta. In a career spanning more than four decades, Tom has been a faculty member and administrator at the University of South Carolina, Arizona State University and Georgia Tech. He has published extensively on the combinatorics of partially ordered sets, graph theory, Ramsey theory and extremal combinatorics. His monograph on dimension theory for partially ordered sets has been in print for nearly 25 years. Tom is an avid movie buff, fan of the New York Yankees and golfer.

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