Generalizations of Determinant Divisibility in Structured Matrices
DOI:
https://doi.org/10.5281/zenodo.18063828Keywords:
Divisibility, Determinant, MatricesAbstract
We study the divisibility properties of determinants in square matrices, with emphasis on structured integer matrices such as Toeplitz, circulant, and Vandermonde forms. We derive explicit conditions under which determinant divisibility follows from the underlying row or column construction rules, uncovering new algebraic relationships between matrix structure and determinant factors. The results extend earlier work on general integer matrices and provide a unified framework for analyzing determinant divisibility in structured settings. Although the probabilistic case of random matrices is noted as a potential direction, the present study focuses on deterministic classes. The findings contribute to a deeper theoretical understanding of determinant behavior and offer insights applicable to combinatorial matrix theory, number theory, and related mathematical disciplines.
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