5 papers
A proof of Haemers' toughness conjecture
Gary Greaves, Haoran Zhu
We prove that if is a connected graph with minimum degree and Laplacian eigenvalues , then the toughness of is bounded be…
A note on some spectral properties of generalised pancake graphs
Gary R. W. Greaves, Haoran Zhu
We prove that the spectral gap of generalised pancake graphs is strictly less than 2 and strictly less than 1 for burnt pancake graphs. In addition, we establish lower bounds on th…
Vertex operators, infinite wedge representations, and correlation functions of the t-Schur measure
Gary Greaves, Naihuan Jing, Haoran Zhu
We study the -Schur measure on partitions, defined by , where denotes the -Schur symmetric functions and the or…
Kronecker coefficients and Harrison centres of the representation ring of the symmetric group
Jia-Cheng Sun, Chi Zhang, Haoran Zhu
We present a computational approach to studying the structure of the representation ring of the symmetric group in dimension six. The Kronecker coefficients and all power formulae…
A generalization of Boole's formula derived from a system of linear equations
Haoran Zhu
We analyze a system of linear algebraic equations whose solutions lead to a proof of a generalization of Boole's formula. In particular, our approach provides an elementary and sho…