1,443 research outputs found
Lexicographic cones and the ordered projective tensor product
We introduce lexicographic cones, a method of assigning an ordered vector
space \Lex(S) to a poset , generalising the standard lexicographic cone.
These lexicographic cones are then used to prove that the projective tensor
cone of two arbitrary cones is a cone, and to find a new characterisation of
finite-dimensional vector lattices.Comment: 8 page
Transversal Lattices
A flat of a matroid is cyclic if it is a union of circuits; such flats form a
lattice under inclusion and, up to isomorphism, all lattices can be obtained
this way. A lattice is a Tr-lattice if all matroids whose lattices of cyclic
flats are isomorphic to it are transversal. We investigate some sufficient
conditions for a lattice to be a Tr-lattice; a corollary is that distributive
lattices of dimension at most two are Tr-lattices. We give a necessary
condition: each element in a Tr-lattice has at most two covers. We also give
constructions that produce new Tr-lattices from known Tr-lattices.Comment: 12 pages; 5 figure
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