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Article overview
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Dimension groups and linear Diophantine inequalities | David Handelman
; Damien Roy
; | Date: |
2 Aug 2015 | Abstract: | Solvability of systems of linear diophantine inequalities is related to
dimension group properties, yielding necessary and sufficient conditions.
Specifically, if $H$ is a subgroup of Euclidean space, for every $h$ in $H$ and
positive integer $m$, for every $epsilon > 0$, we can solve for $x$ in $H$ the
inequalities $h-mx > -epsilon$ coordinatewise, iff for $F$ defined as the
smallest face of the standard simplex (in the dual of the Euclidean space) that
contains the positive linear functionals killing $H$, for all $f$ in $F$, the
subgroup of the reals, $f(H)$, is either zero or dense. | Source: | arXiv, 1508.0195 | Services: | Forum | Review | PDF | Favorites |
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