**Yee’s Bijective Proof of Bousquet-Mélou And Eriksson’s Reﬁnement of the Lecture Hall Partition Theorem**

** **

**Beril Talay**

Mathematics, MSc. Thesis, 2018

**Thesis Jury**

Assoc.Prof Kağan Kurşungöz (Thesis Advisor), Asst. Prof. Dr. Ayesha Asloob Qureshi,

Asst. Prof. Dr. Zafeirakis Zafeirakopoulos

**Date & Time:** 30th, 2018 – 12:00

**Place: **FENS 2008

**Keywords : **integer partition, lecture hall partitions, partition bijection, partition analysis

** **

**Abstract**

** **

A partition λ=(λ_1,λ_2,…,λ_n) of a positive integer N is a lecture hall partition of length n if it satisﬁes the condition 0≤ λ_1/1 ≤ λ_2/2 ≤⋯≤ λ_n/n.

Lecture hall partitions are introduced by Bousquet-Mélou and Eriksson, while studying Coxeter groups and their Poincaré series. Bousquet-Mélou and Eriksson showed that the number of lecture hall partitions of length n where the alternating sum of the parts is k equals to the number of partitions into k odd parts which are less than 2n by a combinatorial bijection. Then, Yee also proved the fact by combinatorial bijection which is diﬀerently deﬁned for of the one of the bijections that suggested by Bousquet-Mélou and Eriksson. In this thesis we give Yee’s proof with details and further possible problems which arises from a paper of Corteel et al.