Abstract:
Given a poset P, a plane partition of shape P is an order preserving map from P to the nonnegative integers. A result of Proctor states that a rectangular poset and its associated trapezoidal poset have the same number of plane partitions of each height. We give a new bijective proof of this result using a tool from dynamical algebraic combinatorics called rowmotion. This bijection arises as the tropicalization of an equivariant birational map between labelings of the rectangle and trapezoid with respect to birational rowmotion, which also proves a conjecture of Williams that birational rowmation on trapezoidal posets has finite order. Joint work with Joseph Johnson.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974