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Aug 21, 2023 at 20:44 history edited Harry Richman CC BY-SA 4.0
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Aug 19, 2023 at 16:30 comment added Brian Hopkins I've seen these called meet matrices (there are also join matrices and combined meet and join matrices). A specific matrix with a related definition is Lehmer's matrix $a_{i,j} = \min\{i,j\} / \max\{i,j\}$ that he asked about in a 1946 Monthly problem (v53, 534-535).
Aug 19, 2023 at 1:39 comment added Benjamin Steinberg These are paratrophic matrices for the semigroup algebra of the semilattice. They are the intertwiners between the left regular representation and the transpose of the right regular representation of the semilattice.
Aug 19, 2023 at 1:22 history answered Friedrich Knop CC BY-SA 4.0