Speaker:  Evan Henning

Title:  The incidence Hopf algebra of the non-crossing partition lattice

Abstract:

First studied in the literature by H.W Becker as planar rhyme schemes, non-crossing partitions have long been a combinatorial object of interest. It is well known that the set of non-crossing partitions of [n] inherit a lattice structure as a sublattice of the partition lattice ordered by refinement. Simion and Ullman showed that this lattice is self-dual. Moreover, intervals in the non-crossing partition lattice factor nicely hence the incidence Hopf algebra on the family of intervals of the non-crossing partition lattice has a nice structure. In this talk we will discuss Hillary Einziger's contributions to the study of the structure of this incidence Hopf algebra. In doing so we will find multiple bases, various formulas for the antipode, and show a bijection between this Hopf algebra and that of the symmetric functions.

https://sites.google.com/view/discretecatsseminar/

Speaker:  Evan Henning

Title:  The incidence Hopf algebra of the non-crossing partition lattice

Abstract:

First studied in the literature by H.W Becker as planar rhyme schemes, non-crossing partitions have long been a combinatorial object of interest. It is well known that the set of non-crossing partitions of [n] inherit a lattice structure as a sublattice of the partition lattice ordered by refinement. Simion and Ullman showed that this lattice is self-dual. Moreover, intervals in the non-crossing partition lattice factor nicely hence the incidence Hopf algebra on the family of intervals of the non-crossing partition lattice has a nice structure. In this talk we will discuss Hillary Einziger's contributions to the study of the structure of this incidence Hopf algebra. In doing so we will find multiple bases, various formulas for the antipode, and show a bijection between this Hopf algebra and that of the symmetric functions.

https://sites.google.com/view/discretecatsseminar/

Speaker:  Maxwell Hosler

Title:  TBA

Abstract:

Speaker:  Maxwell Hosler

Title:  TBA

Abstract:

Speaker:  Richard Ehrenborg, University of Kentucky

Title:  Spanning trees and period polynomials

Date:  September 8, 2025

Abstract:

We determine the number of spanning trees in several graphs which are defined using number theoretic means. Our main example is a generalization of the Paley graph in the case when e = 2. The vertex set is the finite field F_q, where two elements are connected by an edge if their difference belongs to a certain collection of cosets of the eth power subgroup. Using results of Myerson on period polynomials, we obtain explicit formulas when the power e is 3 and 4. This is joint work with David Leep.

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