A LATTICE-THEORETIC GENERALIZATION OF THE LEHMER MATRIX

Abstract

In this paper, we present a lattice-theoretic generalization of the Lehmer matrix. We obtain some certain formulae for the determinant and the entries of the inverse of this new generalization by using lattice-theoretic tools. These formulae are generalization of formulae for the determinant and the inverse of the classical Lehmer matrix and most of its generalizations presented in the literature.

Keywords

• the Lehmer matrix
• lattice
• meet matrix
• determinant
• inverse
• Möbius inversion.

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