Title of the course: Integer Partitions (Tamsayı Parçalanışları)
Instructor: Assoc. Prof. Kağan Kurşungöz
Institution: Sabancı Ü.
Dates: 10-23 Jult 2017
Prerequisites: Some acquaintance with infinite series and convergence. Having taken a course on discrete mathematics is also preferable.
Level: Graduate, advanced undergraduate
Abstract: Definition of integer partitions and partition identities. Basic identities such as Euler or Glaisher along with their combinatorial proofs.
Partition generating functions, q-series, q-series identities and integer partition interpretations (e.g. Euler’s pentagonal number theorem).
Restricted partitions and Gaussian polynomials (a.k.a. q-binomial coefficients). Finite analogues of some partition identities. Lecture hall partitions.
Rogers-Ramanujan identities (as time allows).
Textbook or/and course webpage: Integer Partitions by G. Andrews and K. Eriksson.