Description

Speaker: G. Arunkumar

Date & Time : Monday Feb 26, at 11:30am

Venue: Ramanujan Hall

Title: Chromatic polynomials and Lie algebras

Abstract: In this talk, I will prove a connection between root

multiplicities for Borcherds-Kac-Moody

algebras and graph coloring. I will show that the generalized

chromatic polynomial of the graph

associated to a given Borcherds algebra can be used to give a closed

formula for certain root

multiplicities. As an application, using the combinatorics of Lyndon

words, we construct a basis for the root spaces corresponding to these

roots and determine

the Hilbert series in the case when all simple roots are imaginary.

In last ten minutes, We will talk about chromatic discriminant of a graph:

The absolute value of the coefficient of q in the chromatic polynomial

of a graph

G is known as the chromatic discriminant of G and is denoted

$\alpha(G)$. We start with a brief survey on many interesting

algebraic and combinatorial interpretations of $\alpha(G)$. We use two

of these interpretations (in terms of

acyclic orientations and spanning trees) to give two bijective proofs

for a recurrence formula

of $\alpha(G)$ which comes from the Peterson recurrence formula for

root multiplicities of Kac-Moody algebras.

Date & Time : Monday Feb 26, at 11:30am

Venue: Ramanujan Hall

Title: Chromatic polynomials and Lie algebras

Abstract: In this talk, I will prove a connection between root

multiplicities for Borcherds-Kac-Moody

algebras and graph coloring. I will show that the generalized

chromatic polynomial of the graph

associated to a given Borcherds algebra can be used to give a closed

formula for certain root

multiplicities. As an application, using the combinatorics of Lyndon

words, we construct a basis for the root spaces corresponding to these

roots and determine

the Hilbert series in the case when all simple roots are imaginary.

In last ten minutes, We will talk about chromatic discriminant of a graph:

The absolute value of the coefficient of q in the chromatic polynomial

of a graph

G is known as the chromatic discriminant of G and is denoted

$\alpha(G)$. We start with a brief survey on many interesting

algebraic and combinatorial interpretations of $\alpha(G)$. We use two

of these interpretations (in terms of

acyclic orientations and spanning trees) to give two bijective proofs

for a recurrence formula

of $\alpha(G)$ which comes from the Peterson recurrence formula for

root multiplicities of Kac-Moody algebras.

Description

Ramanujan Hall, Department of Mathematics

Date

Mon, February 26, 2018

Start Time

11:30am IST

Priority

5-Medium

Access

Public

Created by

DEFAULT ADMINISTRATOR

Updated

Sun, February 25, 2018 1:32pm IST