MATH 695 - Introduction to Algebraic Combinatorics

(3 units)

Walks in Graphs, Posets and Sperner Property, Partitions of integers, Enumeration under Group Action, Young Tableaux, Enumeration problems in Graph Theory: Spanning Trees, Eulerian circuits, Matchings and Path-systems, Vector Spaces in Graphs, Dimension and Polynomial methods in Combinatorics, Algebraic Combinatorics Gems.

Maximum units a student may earn: 3

Recommended Preparation: MATH 685.

Grading Basis: Graded
Units of Lecture: 3
Offered: Every Spring - Even Years

Student Learning Outcomes
Upon completion of this course, students will be able to:
1. demonstrate understanding of combinatorial properties (like Sperner property, unimodality) and its implications in various posets.
2. apply Group-theoretic results like, Burnside’s Lemma and Polya-Redfield counting for enumeration problems involving symmetries.
3. demonstrate use of determinants in some enumeration problems in Graph Theory and its applications.
4. apply other linear-algebraic arguments like rank, dimension, orthogonality, polynomials, etc in various combinatorial problems.
5. use these concepts in their research problems and synthesize combinatorial ideas with other branches of Mathematics.

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