Department of Mathematics


  •  Brendon Rhoades, University of California, San Diego
  •  The combinatorics, algebra, and geometry of ordered set partitions
  •  09/20/2018
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

An {\em ordered set partition} of size $n$ is a set partition of $\{1, 2, \dots, n \}$ 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 $S_n$. We will discuss some combinatorial, algebraic, and geometric aspects of permutations (due to MacMahon, Carlitz, Chevalley, Steinberg, Artin, Lusztig-Stanley, Ehresmann, Borel, and Lascoux-Sch\"utzenberger). We will then describe how these results generalize to ordered set partitions and discuss a connection with the Haglund-Remmel-Wilson {\em Delta Conjecture} in the field of Macdonald polynomials. Joint with Jim Haglund, Brendan Pawlowski, and Mark Shimozono.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science