Yee's bijective proof of Bousquet-Mélou and Eriksson's refinement of the lecture hall partition theorem

Official URL: http://risc01.sabanciuniv.edu/record=b1817048 (Table of Contents)

A partition (...) of a positive integer N is a lecture hall partition of length n if it satisfies the condition (...). Lecture hall partitions are introduced by Bousquet-Mélou and Eriksson, while studying Coxeter groups and their Poincare 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 one of the bijections that were suggested by Bousquet-Mélou and Eriksson. In this thesis we give Yee’s proof with details and further possible problems which arise from a paper of Corteel et al.