# Mathematics Colloquia and Seminars

We begin with an elementary bijection among subsets of monotone triangles (aka gog triangles) and fundamental domains of totally symmetric self-complementary plane partitions (aka magog triangles). To make sense of these subsets on the monotone triangle side, we introduce a new class of objects, which we call gog words'' and show that gog words which avoid the pattern 312 are precisely those in bijection. We will then estimate the number of these 312-avoiding gog words for large $n$. Along the way, we will encounter more familiar objects such as semi-standard Young tableaux. This is joint work with Robert Cori and Dominique Gouyou-Beauchamps.