Combinatorics: The Rota Way

Dr Joseph P. S. Kung is Professor of Mathematics at the University of North Texas. He is currently an editor-in-chief for the journal Advances in Applied Mathematics. Gian-Carlo Rota (1932–1999) was a Professor of Applied Mathematics and Natural Philosophy at the Massachusetts Institute of Technology. He was a member of the National Academy of Science. He was awarded the 1988 Steele Prize of the American Mathematical Society for his 1964 paper 'On the Foundations of Combinatorial Theory I. Theory of Moebius Functions.' He was the founding editor of the Journal of Combinatorial Theory. Catherine H. Yan is a Professor of Mathematics at Texas A & M University. She was a Courant Instructor at New York University (1997–1999) and a Sloan Fellow (2001–2003).

• 1. Sets, functions, and relations; 2. Matching theory; 3. Partially ordered sets and lattices; 4. Generating functions and the umbral calculus; 5. Symmetric functions and Baxter algebras; 6. Determinants, matrices, and polynomials; 7. Selected solutions.

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