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Pattern Avoidance and Monotone Triangles

Algebra & Discrete Mathematics

Speaker: Arvind Ayyer, UC Davis
Location: 1147 MSB
Start time: Fri, Feb 11 2011, 2:10PM

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.