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q,t- Catalan numbers

Student-Run Applied & Math Seminar

Speaker: Kirill Paramonov, UC Davis Mathematics
Location: 2112 MSB
Start time: Tue, Nov 24 2015, 12:10PM

Generalized q,t-Catalan number is one of the numerous objects arising from the fusion of algebra and combinatorics. On one hand, it is given by the bigraded Hilbert series of the space of diagonal harmonics. On the other hand, q,t-Catalan number is given by the sum over all Dyck paths of certain statistics. I'm going to talk about some interesting combinatorial results related to q,t-Catalan numbers, present few open problems and discuss the way to approach those problems.