MATH501 Introduction to Combinatorial Theory, Fall 2009
This course is an introduction to Combinatorics
aimed at first year graduate students.
The goal is to learn about both methods and structures.
Methods includes things like counting tools
and procedures like the lexicographical
ordering, but also includes
permutation groups and algorithms.
Structures includes objects that arise often in combinatorics
(sets, set-systems, bit-strings,
graphs a.k.a. networks,
trees, partitions, examples of partial orderings, lattices,
Latin Squares, designs, codes,
Often it is the interplay between the structures and the methods that
make combinatorics interesting and fun. Because of that, it is reasonable
to study methods and structures somewhat intertwined (as opposed to say,
completely separate). This is what we will do this time around.
- Call Number 63396
Instructor: Anton Betten, room 207, Weber building.
Email lastname at math dot colostate dot edu
Course website: http://www.math.colostate.edu/ betten/courses/MATH501/FA09/501_syllabus.html http://www.math.colostate.edu/~betten/courses/MATH501/FA09/501_syllabus.html
Class: M W F 3 - 3:50 pm, ENGRG E 206
Text: Combinatorial Methods with Computer Applications, Jonathan Gross, Chapmann and Hall / CRC.
ISBN13: 978-1-58488-743-0 (Hardcover).
Homework: Assigned bi-weekly, due Wednesdays
Projects: You will do one project that either involves programming or
a more theoretical part with write-up.
Final Exam: As scheduled by the registrar's office.
Monday 1pm, Friday 1pm
Week 1: Binomial coefficients, bitstrings, power set, Binomial Theorem.
Week 2: The lexicographic order, ranking unranking, power set.
Week 3: Projective planes (mostly finite), Desargues,
projective geometry (mostly finite).
Week 4: More on binomial coefficients, arrangements and selections,
multinomial coefficients. Pigeonhole principle.
Weeks 5 and 6: Fibonacci and Catalan, Generating functions.
Week 7: Permutations, order tree, Dijkstra's
algorithm for the lexicographic successor.
Week 8: Derangements, Inclusion-Exclusion, Euler's totient function.
Weeks 9 and 10: Graph theory: Euler, Petersen, Hamming, Relations, digraphs, graphs and tournaments.
Landau, Payley. Trees. Bipartite graphs. Hamiltonian graphs.
Week 11: Automorphism groups. Degree sequence. Labelled trees (Cayley's Theorem),
Pruefer code. Havel/Hakimi. Matchings. Cayley graphs.
Weeks 12 and 13: Strongly regular graphs, parameters, bounds. Existence and Nonexistence
Weeks 14 and 15: Network algorithms: Shortest path, minimum cost spanning tree,
Floyd Warshall, max-flow-min-cut, travelling salesman problem.
Your final grade will be determined from a score of 500:
Homework assignment #1
Homework assignment #2
Homework assignment #3
Homework assignment #4
Homework assignment #5
Homework assignment #6
Homework assignment #7
Homework assignment #8
Homework assignment #9
Homework assignment #10
File translated from
On 14 Oct 2009, 13:53.