Equips readers with the fundamentals of enumerative combinatorics with an emphasis on generating function techniques Promotes an engaging learning experience by utilizing Inquiry-Based Learning (IBL) Offers an accessible entry-point to enumerative combinatorics that builds from minimal prerequisites to a selection of advanced topics

Autorentext

T. Kyle Petersen is an Associate Professor of Mathematics at DePaul University, Chicago, USA. His research areas include algebraic, enumerative, and topological combinatorics. He received his PhD in Mathematics from Brandeis University.

Inhalt
0. Introduction to this book.- 1. First Principles.- 2. Permutations.- 3. Combinations.- 4. The Binomial Theorem.- 5. Recurrences.- 6. Generating Functions.- 7. Exponential Generating Functions and Bell Numbers.- 8. Eulerian Numbers.- 9. Catalan and Narayana Numbers.- 10. Refined Enumeration.- 11. Applications to Probability.- 12. Some Partition Theory.- 13. A Bit of Number Theory.- A. Supplementary Exercises.