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arXiv · 1510.06513

On incomplete lattice homomorphisms in subspaces of geometries: "half" a problem of Hartmanis from 1959

Jonathan David Farley·Dominic van der Zypen
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Abstract

Turing Award winner Juris Hartmanis introduced in 1959 lattices of subspaces of generalized partitions ("partitions of type n"; "geometries" if $n = 2$). Hartmanis states it is "an unsolved problem whether there are any incomplete lattice homomorphisms in" lattices of subspaces of geometries. (He continues, "[I]f so how can these geometries be characterized.") We give a positive answer to this question.

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Jonathan David Farley, Dominic van der Zypen. 2015-10-22. On incomplete lattice homomorphisms in subspaces of geometries: "half" a problem of Hartmanis from 1959. https://arxiv.org/abs/1510.06513

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