Combinatorics: Math 630
Fall 2014, MWF 1:50–2:40 in Blocker 202
Professor: Michael Anshelevich, Blocker 533D, manshel@math.tamu.edu.
Webpage: www.math.tamu.edu/∼manshel/m630/m630.html.
Office hours: MWF 12:30–1:30 p.m., or by appointment.
Textbook: Martin Aigner, A COURSE IN ENUMERATION, Springer, ISBN 9783540390329. The
text is available for purchase or download through SpringerLink, accessible through the TAMU
library or from any on-campus computer. A few supplementary topics will be included from
E NUMERATIVE C OMBINATORICS VOLUME I (2nd ed., Richard P. Stanley, Cambridge University
Press), also accessible online through the TAMU library.
Prerequisites: Undergraduate discrete math course or permission of instructor.
Learning Objectives: This is an introduction at the graduate level to the fundamental ideas and
results of combinatorics, including enumerative techniques, sieve methods, partially ordered sets,
and generating functions. The course will provide a one-semester survey of fundamental structures
of combinatorics, and selected topics in combinatorial theory. It will concentrate on methods and
techniques of combinatorial enumeration. It is intended for graduate students in combinatorics and
related fields, such as representation theory, computer science, or probability theory
Preliminary weekly schedule (subject to modification):
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Basic combinatorial structures: subsets, set partitions, permutations (1.1–1.3).
Permutation statistics (Stanley 1.3–1.5).
Number partitions. Lattice paths (1.4, 1.5).
Formal power series and infinite matrices (2.1–2.4).
Generating functions I (2.5, 3.1).
Generating functions II (3.2–3.4).
Inclusion-exclusion. Möbius inversion (5.1–5.2).
Partially ordered sets (Stanley 3.1–3.8).
The involution principle. Hyperplane arrangements. (5.3, Stanley 3.9–3.11).
The Lemma of Gessel-Viennot. Symmetries and patterns (5.4, 6.1).
Enumeration of patterns (6.2–6.4; time permitting).
Matrices, lattice paths, and orthogonal polynomials (7.1–7.3; time permitting).
Symmetric functions (8.1–8.3).
The RSK algorithm (8.4–8.5).
Grading: The grade will be determined by homework (70%, including participation), and a takehome final exam (30%). A total score of 90% or more guarantees an A, a score of 80% or more a
B, 70% or more a C, 60% or more a D.
Homework: Weekly, due on Fridays in class. You are encouraged to work on the homework
together, but straight copying is not allowed. Late homework will not be accepted, but the lowest
assignment score will be dropped.
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Scholastic Dishonesty: Cheating of any form is not acceptable and it will be dealt with harshly.
In particular, copying work done by others, either in-class or out of class, is an act of scholastic
dishonesty and it will be prosecuted to the full extent allowed by university policy. Collaboration on
assignments is permitted for this course, however each student must write up their own solutions.
For more information on university policies regarding scholastic dishonesty, see the University
Student Rules.
Aggie Honor Code: “An Aggie does not lie, cheat, or steal or tolerate those who do.”
Students with disabilities: Come talk to me no later than the first week of classes. “The Americans
with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive
civil rights protection for persons with disabilities. Among other things, this legislation requires
that all students with disabilities be guaranteed a learning environment that provides for reasonable
accommodation of their disabilities. If you believe that you have a disability requiring an accommodation, please contact the Department of Student Life, Services for Students with Disabilities, in
Room 126 of the Koldus Building or call 845–1637.”
Attendance: According to the University Student Rules, absence for three or more class days
requires a University-approved excuse and documentation.
Other important dates: September 5 (last day to add or drop a course), November 21 (Q-drop),
December 8 (last class).
Keys to success: Attend class (of course :) Solve all the homework problems, well before the
exams. Spend more than seven hours per week working on the problems. Form study groups to
discuss the course material and homework problems. Read ahead in the text.
All printed handouts and web-materials are protected by US Copyright Laws. No multiple copies can be
made without written permission by the instructor.