Combinatorics A Guided Tour

ISBN-10: 0883857626
ISBN-13: 9780883857625
Edition: 2010
Authors: David R. Mazur
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Book details

Copyright year: 2010
Publisher: Mathematical Association of America
Binding: Hardcover
Pages: 410
Size: 7.00" wide x 10.00" long x 1.00" tall
Weight: 2.112
Language: English

David R. Mazur is Associate Professor of Mathematics at Western New England College in Springfield, Massachusetts. He was born on October 23, 1971 in Washington, D.C. He received his undergraduate degree in Mathematics from the University of Delaware in 1993, and also won the Department of Mathematical Sciences' William D. Clark prize for 'unusual ability' in the major that year. He then received two fellowships for doctoral study in the Department of Mathematical Sciences (now the Department of Applied Mathematics and Statistics) at The Johns Hopkins University. From there he received his Master's in 1996 and his Ph.D. in 1999 under the direction of Leslie A. Hall, focusing on operations research, integer programming, and polyhedral combinatorics. His dissertation, 'Integer Programming Approaches to a Multi-Facility Location Problem', won first prize in the 1999 joint United Parcel Service/INFORMS Section on Location Analysis Dissertation Award Competition. The competition occurs once every two years to recognize outstanding dissertations in the field of location analysis. Professor Mazur began teaching at Western New England College in 1999 and received tenure and promotion to Associate Professor in 2005. He was a 2000–2001 Project NExT fellow and continues to serve this program as a consultant. He is an active member of the Mathematical Association of America, having co-organized several sessions at national meetings. He currently serves on the MAA's Membership Committee.

Preface
Before you go
Notation
Principles of Combinatorics
Typical counting questions, the product principle
Counting, overcounting, the sum principle
Functions and the bijection principle
Relations and the equivalence principle
Existence and the pigeonhole principle
Distributions and Combinatorial Proofs
Counting functions
Counting subsets and multisets
Counting set partitions
Counting integer partitions
Algebraic Tools
Inclusion-exclusion
Mathematical induction
Using generating functions, part I
Using generating functions, part II
techniques for solving recurrence relations
Solving linear recurrence relations
Famous Number Families
Binomial and multinomial coefficients
Fibonacci and Lucas numbers
Stirling numbers
Integer partition numbers
Counting Under Equivalence
Two examples
Permutation groups
Orbits and fixed point sets
Using the CFB theorem
Proving the CFB theorem
The cycle index and P�lya's theorem
Combinatorics on Graphs
Basic graph theory
Counting trees
Colouring and the chromatic polynomial
Ramsey theory
Designs and Codes
Construction methods for designs
The incidence matrix, symmetric designs
Fisher's inequality, Steiner systems
Perfect binary codes
Codes from designs, designs from codes
Partially Ordered Sets
Poset examples and vocabulary
Isomorphism and Sperner's theorem
Dilworth's theorem
Dimension
M�bius inversion, part I
M�bius inversion, part II
Bibliography
Hints and answers to selected exercises

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