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Graduate topics · Ahmedabad University

Combinatorics of Permutations

Term
TBC
Status
Current
Level
Graduate
Prerequisites
A solid foundation in undergraduate discrete mathematics, combinatorics, and abstract algebra. Familiarity with generating functions and basic group theory is strongly recommended.
Auditing
Auditing students submit all homework sets and keep at least 60% attendance.
σ = 351426, with an occurrence of the pattern 231 highlighted. Here inv(σ) = maj(σ) = 6 — MacMahon proved the two statistics are equidistributed over every Sn.

Course description

Permutations are fundamental objects in discrete mathematics, with deep connections to algebra, probability, and computer science. This graduate-level course explores the combinatorial structure of the symmetric group, covering both classical enumeration and modern structural theories. By integrating geometric, algebraic, and analytic techniques, students investigate how permutations can be decomposed, restricted, and quantified.

The course has two major themes: permutation statistics and q-analogues, and the theory of pattern avoidance.

Grading

  • Assignments 40% — biweekly
  • Mid-semester exam 30% — 120 minutes, written
  • End-semester exam 30% — 180 minutes, written

An A requires at least 80% overall, though 80% does not automatically guarantee one.

Lectures

The lecture log is not up yet. It will be filled in week by week once the term starts.