MATH 630-600. Enumerative Combinatorics

Fall, 2018, MWF 11:30- 12:20 p.m. BLOC 164

    Instructor: Dr. Catherine Yan

    Office: BLOCKER 513F


    Class: MWF 11:30--12:20, BLOC 148

    Office hours: Monday & Wednesday 1-2pm (or by appointment)

    Grade Policy: Grade is determined by Homeworks (including participation).

    Level : Graduate

    Prerequisites : Math 302 (Discrete Mathematics), or Math 431 (Structures and methods in Combinatorics), or equivalent will be sufficient.

    Course Description : This course will be an introduction at graduate level to the fundamental ideas and results of combinatorics. The course moves quickly but does not assume prior study in combinatorics. It is intended for graduate students from mathematics or related areas wanting a good one-semester background in fundamental and applicable discrete mathematics. It also provides solids preparation for advanced combinatorics and for various courses in computer sciences.

    The course will cover structures and methods of combinatorics, including basic counting techniques, sieve methods, generating functions, hypergeometric summation, and special topics on Catalan structures and symmetric functions. One emphasis of the course will be bijective proofs illustrating the frequent, and often surprising, interrelations between these structures. The prerequisite for this course is an undergraduate discrete mathematics course or permission of the instructor.

    Text: : A Course in Enumeration , by Martin Aigner, Springer. ISBN: 978-3-540-39032-9 (Print) 978-3-540-39035-0 (Online)

    Grading: Tne plan is to cover the first eight chapters of Aigner's textbook, on Basics and Methods, together two Topics chapters on the Catalan Connection and Symmetric Functions, We will have homework assignments every couple of weeks, depending on our progress in class. As exercise is an important part of combinatorics, anyone who misses three homework sets fails the course automatically. No late home work will be accepted except for university-approved excuses.

    The grade will be determined by the homework assignments (90%) and in-class participation (10%).
    The standard cutoffs for letter grades will be used:
    A 90/100; B 80/100; C 70/100; D 60/100.

    First day Handout

    Homework Assignments

    Useful Identities This list will be updated periodically.

    Homework will be assigned every couple of weeks, depending on how much we cover in lectures. The following due dates are tentative.
    Homework Assignments and Solutions will be distributed through class mailing list.

    Homework 0. Due on September 3. Please send a short introduction of yourself to,

    Homework 1. Due on September 7.

    Homework 2. Due on September 19.

    Homework 3. Due on October 1.

    Homework 4. Due on October 12.

    Homework 5. Due on October 24.

    Homework 6. posted. Due on November 5.

    Homework 7. posted. Due on November 16.

    Homework 8. This is for you to practice.

    The optional mini-project is due on Dec 5th.

    Dec. 5th is reserved as a make-up day.

    Lecture Schedule

    (subject to change without notice)

    Fundamental Coefficients, Stirling numbers, permutation statistics, set and integer partitions. twelve-fold way, lattice paths: 3 wks

    Formal Series and Infinite Matrices: 1 wk

    Generating Functions, tree counting, Lagrange inversion formula: 2.5 wk

    Hypergeometric Summmation: 0.5 wk, maple sheet.

    Sieve Methods, Mobius inversion, involution principle, Gessel-Viennot Lemma: 3 wk

    Number of patterns and Polya counting: 1 wk

    Catalan numbers and structures: 1.5 wk

    Symmetric polynomials and functions: 1.5 wk

    Note: Nov. 21, 23: Thanksgiving holidays, No class.

    Dec. 5th is a make-up day.

    MAKE-UP POLICY: Make-ups for missed quizzes and exams will only be allowed for a university approved excuse in writing. Wherever possible, students should inform the instructor before an exam or quiz is missed. Consistent with University Student Rules , students are required to notify an instructor by the end of the next working day after missing an exam or quiz. Otherwise, they forfeit their rights to a make-up.

    POLICY FOR ABSENCES: Attendance on a regular basis is expected. While there are occasionally good reasons for you to choose to miss class, my experience has been that there is a strong correlation between attendance (as long as you are awake and listening) and performance in the course.

    For absence related to injure or illness, students who are absent from class three or more days should provide instructors with confirmation from a medical provider for an excused absence.

    COPYRIGHT POLICY: All printed materials disseminated in class or on the web are protected by Copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

    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 you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information, visit .

    SCHOLASTIC DISHONESTY: Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. Collaboration on assignments, either in-class or out-of-class, is forbidden unless permission to do so is granted by your instructor. For more information on university policies regarding scholastic dishonesty, see University Student Rules .


    ``An Aggie does not lie, cheat, or steal or tolerate those who do."

    CHEATING IS FORBIDDEN Students who cheat will be reported to the Dean with a recommendation that their course grade be set at F. The dean may take further action, including expulsion from the university.