Some properties of row-adjusted meet and join matrices

Abstract

Let (P, ⪯) be a lattice, S a finite subset of P and f ₁, f ₂, … , f _n complex-valued functions on P. We define row-adjusted meet and join matrices on S by and . In this article, we determine the structure of the matrix in general case and in the case when the set S is meet closed we give bounds for and present expressions for and . The same is carried out dually for row-adjusted join matrix of a join-closed set S.

Keywords:

• meet matrix
• join matrix
• GCD matrix
• LCM matrix
• Smith determinant

AMS Subject Classifications::

• 11C20
• 15B36
• 06B99

Acknowledgements

The authors wish to thank the referee for careful reading and useful comments.