Topic:Asymptotic normality criteria of coefficients of a polynomial and their applications in combinatorics
Speaker: Research Fellow Ye Yongnan
Event date: 5/7/2019
Event time: 16:00 p.m.
Venue: Lecture Hall 1506, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract: The asymptotic distribution theory for coefficients of a polynomial is an active topic inasymptotic analysis. In 1967, Harper proposed a criterion to measure theasymptotic normality of a series of numbers, when he researched the asymptoticbehavior of Stirling numbers of the second kind. In this talk, we will discusssome further asymptotic normality criteria of coefficients of apolynomial withall real roots or purely imaginary roots (including 0). These new asymptoticnormality criteria turn out to be very efficient and have abundant applicationsin combinatorics, mainly including the coefficients of aseries ofcharacteristic polynomials of adjacency matrix, Laplacian matrix,signlessLaplacian matrix, skew-adjacency matrix, chromatic polynomial, and some graphnumbers, such as matching numbers, independence numbers, clique numbers. Amongwhich, we generalize and verify some conjectures about asymptotic normality incombinatorics, e.g., the matching numbers proposed by Godsil and Kahn, the(signless) Laplacian coefficients claimed by Wang et al.