4 papers · 1 filter
Graphs with three eigenvalues from group divisible designs
Gary Greaves, Jose Yip
We construct biregular graphs with three distinct eigenvalues from semiregular group divisible designs. For every prime power , we use the spectral structure of Muzychuk's Const…
Quantum entropy and the Bannai--Ito multiplicity conjecture
Gary Greaves, Haoran Zhu
We prove that the multiplicities of every symmetric -polynomial association scheme form a log-concave sequence. This resolves the 1984 unimodality conjecture of Bannai and Ito a…
Neumaier graphs of coherent rank five
Gary Greaves, Zhao Kuang Tan
We construct an infinite family of Neumaier graphs of coherent rank five, answering the existence question at the smallest possible coherent rank beyond the strongly regular case.…
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 ordinar…