G. Greaves

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20242026

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math.CO2025

Characteristic polynomials of ${\pm 1}$ -matrices modulo a power of $2$

Gary Greaves, Huu An Phan

For a fixed integer $e ⩾ 3$ and $n$ large enough, we show that the number of congruence classes modulo $2^{e}$ of characteristic polynomials of $n \times n$ symmetric $\{\pm…

math.CO2025

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…

math.CO2025

Neumaier graphs from cyclotomy with small coherent rank

Gary R. W. Greaves, Zhao Kuang Tan

Using cyclotomy, we construct a new infinite family of Neumaier graphs that includes infinitely many strongly regular graphs. Notably, this family conjecturally contains infinitely…

Characteristic polynomials of {±1}-matrices modulo a power of 2

A note on some spectral properties of generalised pancake graphs

Neumaier graphs from cyclotomy with small coherent rank

Characteristic polynomials of ${\pm 1}$ -matrices modulo a power of $2$