Common tiling complements in large-prime extensions of finite cyclic groups
Year: 2026
Type: preprint
Abstract: Let R ≥ 2 and let q > R be prime. We prove that the common tiling-complement property for all families of sets with a fixed spectrum is equivalent in the cyclic groups of orders R and qeR for every e ≥ 1. The proof expands the shared spectrum and all its sources by complementary digits. A rank estimate then shows that every terminal frequency fiber is a spectrum of every terminal source fiber. A separate stacking argument relates the common-complement property at order R to spectral tiling at order qR. These results can be iterated along a chain of successively large prime powers.
Author: Liang, Jiahui
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225653321
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