Yee’s Bijective Proof of Bousquet-Mélou And Eriksson’s Reﬁnement of the Lecture Hall Partition Theorem
Mathematics, MSc. Thesis, 2018
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
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.