The Refined Lecture Hall Theorem via Abacus Diagrams
  Bousquet-M\'elou & Eriksson's lecture hall theorem generalizes Euler's celebrated distinct-odd partition theorem. We present an elementary and transparent proof of a refined version of the lecture hall theorem using a simple bijection involving abacus diagrams. 
Laura Bradford, Meredith Harris, Brant Jones, Alex Komarinski, Carly   Matson, Edwin O'Shea
math.CO