Steep tilings and sequences of interlaced partitions

We present a general bijection between a family of domino tilings (the 
so-called "steep tilings") and sequences of partitions where, at each 
step, one adds or removes an horizontal or vertical strip. As particular 
cases, we recover domino tilings of the Aztec diamond and pyramid 
partitions. We will discuss some applications concerning enumeration, 
asymptotic shapes and random generation. Based on joint work with Sylvie 
Corteel, Guillaume Chapuy and later on with Cédric Boutillier, Dan 
Betea, Sanjay Ramassamy and Mirjana Vuletić.