New York Journal of Mathematics
Volume 30 (2024), 307-322


Livio Liechti

On the minimal spectral radii of skew-reciprocal integer matrices

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Published: February 17, 2024.
Keywords: minimal spectral radius, integer matrix, irreducible matrix, primitive matrix, skew-reciprocal matrix, curve graph, clique polynomial.
Subject [2020]: 15B48,15B36, 11R06, 05C31, 57K20.

In this paper we determine the minimal spectral radii among all skew-reciprocal integer matrices of a fixed even dimension that are primitive or nonnegative and irreducible. In particular, except for dimension six, we show that each such class of matrices realises smaller spectral radii than the corresponding reciprocal class.


The author thanks Chi Cheuk Tsang and an anonymous referee for their comments on a first version of this article.

Author information

Livio Liechti
Department of Mathematics
University of Fribourg
Chemin du Musée 23
1700 Fribourg, Switzerland