A simple explicit bijection between (n,2) Gog and Magog trapezoids

Abstract

A sub-problem of the open problem of finding an explicit bijection between alternating sign matrices and totally symmetric self-complementary plane partitions consists in finding an explicit bijection between so-called $(n,k)$ Gog trapezoids and $(n,k)$ Magog trapezoids. A quite involved bijection was found by Biane and Cheballah in the case $k=2$. We give here a simpler bijection for this case.