Ercan Altınışık, Fatih Yağcı, Mehmet Yıldız
1.584 417


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.


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

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M. Aigner, Combinatorial Theory, Springer-Verlag, 1979.

I. Akkuş, The Lehmer matrix with recursive factorial entries, Kuwait J. Sci, 42 (2015), no. 2, 34–41.

B.V.R. Bhat, On greatest common divisor matrices and their applications, Linear Algebra Appl. 158 (1991) 77-97.

R. Bhatia, Min matrices and Mean matrices, Math. Intelligencer 33, no.2 (2011) 22-28.

E. Kılıç, P. Stanica, The Lehmer matrix and its recursive analogue, J. Combinat. Math and Combinat. Computing 74 (2010) 193-207.

I. Korkee, P. Haukkanen, On meet and join matrices associated with incidence functions, Linear Algebra Appl. 372 (2003) 127-153.

D. H. Lehmer, Problem E710, Amer. Math. Monthly, 53 (1946) p.97.

M. Marcus, Basic Theorems in Matrix Theory, Nat. Bur. Standarts Appl. Math. Ser 57 (1960) 21-24.

M. Mattila, On the eigenvalues of combined meet and join matrices, Linear Algebra Appl. 466 (2015) 1-20.

M. Mattila, P. Haukkanen, Studying the various properties of MIN AND MAX matrices –elementary vs. more advanced methods, Spec. Matrices 4 (2016), Art. 10.

M. Newman, J. Todd, The evaluation of matrix inversion programs, J. Society Industrial and Appl. Math. 6 (1958) 466-476.

L. F. Shampine, The condition of certain matrices, J Res. Natl. Inst. Stan. B Mathematics and Mathematical Physics 69B no.4 (1965) 333-334.

D. M. Smiley and M. F. Smiley, and J. Williamson, Amer. Math. Monthly, 53 (1946) 534-535.