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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, March 29, 2018 - 3:00pm

Dun Qiu

UC San Diego


University of Pennsylvania


Shuffle Conjecture of Haglund, Haiman, Loehr, Remmel, and Ulyanov in 2005 is a formula between symmetric function $\nabla e_n$ and statistics on parking functions, which was proved by Carlsson and Mellit. Then in 2015, Haglund, Remmel and Wilson gave two conjectures , called the Delta Conjecture, for the delta operator expression $\Delta'_{e_k}e_n$, which is a generalization of the Shuffle Conjecture. Our work is mainly focusing on the expression $\Delta'_{e_k}\Delta_{h_r}e_n$, for which we have two conjectures analogues to the Delta Conjecture. We will also show some combinatorial connections between the combinatorial side of our conjectures and ordered multiset partitions.