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Penn Mathematics Colloquium

Wednesday, April 4, 2018 - 3:30pm

Brendon Rhoades

UC San Diego


University of Pennsylvania


Tea before the talk at 3pm in the math lounge, fourth floor DRL.

An ordered set partition of size n is a set partition of {1, 2, ... , n} with a specified order on its blocks. When the number of blocks equals the number of letters n, an ordered set partition is just a permutation in the symmetric group. We will discuss some combinatorial, algebraic, and geometric aspects of permutations (due to MacMahon, Carlitz, Chevalley, Steinberg, Artin, Garsia-Stanton, Lusztig-Stanley, Ehresmann, Borel, and Lascoux-Schutzenberger). We will then describe how these results generalize to ordered set partitions and discuss a connection with the Haglund-Remmel-Wilson Delta Conjecture in the field of Macdonald polynomials. Joint with Jim Haglund, Brendan Pawlowski, and Mark Shimozono.