1, 2, 7, 42, 429, 7436...

This sequence appeared for the first time in the study of Alternating Sign Matrices at the beginning of the 80'. With time, mathematicians and physicists got used to seeing this mysterious sequence appear counting sets apparently so different.

In this talk I will speak about three such sets: alternating sign matrices; plane partitions; and, completely packed loops. We will try to understand the relations between those objects.
If the public feels courageous enough, we will discuss some technical tools, notably the quantum Knizhnik--Zamolodchikov equation which allowed us to obtain some particular results.