Inquiry-Based Enumerative Combinatorics

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

Auteur

T. Kyle Petersen is Professor of Mathematics at DePaul University in Chicago. His research interests lie in algebraic, enumerative, and topological combinatorics, and he has been an active member of the Inquiry-Based Learning (IBL) community for over a decade. His graduate textbook, Eulerian Numbers, appears in Birkhäuser Advanced Texts Basler Lehrbücher.

Contenu

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.