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On meet matrices on posets. (English) Zbl 0870.15016

The author considers the meet matrices on posets as a generalization of the greatest common divisor (GCD) matrices. Some of the most important properties of GCD matrices are expressed in the language of meet matrices. The author proves a structure theorem for meet matrices, derives explicit expressions and bounds for the determinants of meet matrices, and finally considers the inverse of meet matrices.

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
11C20 Matrices, determinants in number theory
15A15 Determinants, permanents, traces, other special matrix functions
15A09 Theory of matrix inversion and generalized inverses
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