Beschreibung:
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, the book presents an introduction to enumerative and algebraic combinatorics emphasizing bijective methods.
PART 1: ENUMERATION. Chapter 1: Basic Counting; Chapter 2: Combinatorial Identities and Recursions; Chapter 3: Counting Problems in Graph Theory; Chapter 4: Inclusion-Exclusion and Related Techniques; New Chapter 5: Generating Functions; Chapter 6: Ranking, Unranking, and Successor Algorithms; PART 2: ALGEBRAIC COMBINATORICS; Chapter 7: Permutation Statistics and q-Analogues; Chapter 8: Permutations and Group Actions; Chapter 9: Tableaux and Symmetric Polynomials. Chapter 10: Abaci and Antisymmetric Polynomials; Chapter 11: Additional Topics. New Appendix: Background in Abstract Algebra.