2025/09/22 by Szymański, Jakub · 1 citation
#20F65 #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2509.17823
In this article, we explore the problem of constructing high-dimensional expanders through the study of relations between expansion constants over different rings. We investigate expansion constants of integer matrices regarded as morphisms between free modules over ℝ, ℤ, and ℤ/pℤ. We introduce a new condition which we call integral spanning regarding kernels of integer matrices, and prove that it ensures equality of real and integral expansions. In addition, we prove a bound on expansion constants over finite fields for a certain class of matrices in terms of the corresponding integral expansions. As an application, one may use this theorem to bound the expansion of codifferentials over ℤ/2ℤ in degrees 0 and 1.