Generalizations of the Maillet Determinant
Youngmi Hur, Zachary Lubberts
TL;DR
This paper explores extensions of the Maillet determinant, analyzing the properties of the associated matrices, including eigenvalues and eigenvectors, to derive new formulas for these determinants.
Contribution
It introduces several extensions of the Maillet determinant and provides explicit eigenvalues and eigenvectors for the resulting matrices.
Findings
Eigenvalues and eigenvectors of the extended matrices are computed.
New formulas for the generalized Maillet determinants are derived.
Properties of the underlying matrices are characterized.
Abstract
We consider several extensions of the Maillet determinant studied by Malo, Turnbull, and Carlitz and Olson, and derive properties of the underlying matrices. In particular, we compute the eigenvectors and eigenvalues of these matrices, which yield formulas for these new determinants.
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Taxonomy
TopicsAdvanced Topics in Algebra · Graph theory and applications · Tensor decomposition and applications