Monday, October 24, 2016 at 3:00 PM in SAS 4201
Ricky Liu, NC State
Positive expressions for skew divided difference operators
For any pair of permutations, Macdonald defines a skew divided difference operator and shows how these operators can be used to compute the structure constants for Schubert polynomials. We will show that any skew divided difference operator can be written explicitly as a polynomial in the degree 1 divided difference operators with positive coefficients, which settles a conjecture of Kirillov. The proof relies on various tools from the braided Hopf algebra structure of the Fomin-Kirillov algebra.
Monday, November 7, 2016 at 3:00 PM in SAS 4201
Naihuan Jing, NC State
Monday, November 21, 2016 at 3:00 PM in SAS 4201
Emily Meehan, NC State
In this talk, we define a family of combinatorial objects, which we call Baxter posets. We prove that the Baxter numbers count Baxter posets by demonstrating that Baxter posets are the adjacency posets of diagonal rectangulations. Several known families of Baxter objects are closely related to Catalan combinatorics, and we motivate the definition of Baxter posets by summarizing some of these relationships. Given a diagonal rectangulation, we will describe the cover relations in the associated Baxter poset. We will also describe a method for obtaining the Baxter permutation associated to a Baxter poset.
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