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 Events
UBC
Tue 19 Nov 2019, 4:00pm
Discrete Math Seminar
ESB 4127
The e-positivity of chromatic symmetric functions
ESB 4127
Tue 19 Nov 2019, 4:00pm-5:00pm

Abstract

The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, e-positivity.
 
In this talk we approach the question of e-positivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contractible to the claw, and whose chromatic symmetric function is not e-positive.
 
This is joint work with Soojin Cho, Samantha Dahlberg, Angele Foley and Adrian She, and no prior knowledge is assumed.
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University of Queensland
Tue 14 Jan 2020, 4:00pm
Discrete Math Seminar
ESB 4127
Lascoux polynomials and colored vertex models
ESB 4127
Tue 14 Jan 2020, 4:00pm-5:00pm

Abstract

The cohomology ring of the Grassmannian, the set of k-dimensional subspaces in n-dimensional space, can be described by Schur functions, a symmetric function that are characters of the special linear Lie group. To study the K-theory ring, the corresponding objects we use are (symmetric) Grothendieck polynomials. Demazure characters can be considered as partial Schur functions and are characters of representations of the subgroup of upper triangular matrices. The K-theoretic analog of Demazure characters are known as Lascoux polynomials, but they currently have no representation theoretic or geometric interpretation. In joint work with Valentin Buciumas and Katherine Weber, we give the first known combinatorial interpretation for Lascoux polynomials by describing a colored version of the 5-vertex model of Motegi and Sakai. In this talk, we will discuss Lascoux polynomials, the colored 5-vertex model, and the corresponding combinatorial interpretation from our result. No knowledge of the material will be assumed.
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