PhD. Thesis Defense: Burcu Barsakçı, Method of Weighted Words on Cylindric Partitions

Method of Weighted Words on Cylindric Partitions

Burcu Barsakçı
Mathematics, PhD Dissertation, 2025

Thesis Jury

Assoc. Prof. Kağan Kurşungöz (Thesis Advisor)

Assoc. Prof. Mohammad Sadek

Prof. Yücel Saygın

Asst. Prof. Jehanne Dousse

Prof. Mehmet Cenkci

Date & Time: July 10th, 2025 – 11:00 AM

Place: FENS 2019

Zoom Link: https://sabanciuniv.zoom.us/s/94769435384

Keywords: Cylindric partitions, Ordinary partitions, Method of weighted words, Generating functions, Shapes of slices of cylindric partition

Abstract

In this thesis, we study the generating functions of cylindric partitions having profile c=(c₁, c₂, …, c_r) with rank 2 and levels 2, 3 and 4. As a result, we give expressions alternative to Borodin's formula for these generating functions. We use the method of weighted words which was first introduced by Alladi and Gordon, later was applied by Dousse in a new version to prove some partition identities and to get infinite products. We adopt the method to our subject with a more combinatorial approach.