Does imply axiom of choice?
In [7], V. Novak and M. Novotny studied ternary relational structures by means of pairs of binary structures; they obtained the so-called double binary structures. In this paper, the idea is generalized to relational structures of any finite arity.
The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.
The eigenproblem of a circulant matrix in max-min algebra is investigated. Complete characterization of the eigenspace structure of a circulant matrix is given by describing all possible types of eigenvectors in detail.