# Towards Strong Reverse Minkowski-Type Inequalities for Lattices

@article{Dadush2016TowardsSR, title={Towards Strong Reverse Minkowski-Type Inequalities for Lattices}, author={Daniel Dadush and Oded Regev}, journal={2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)}, year={2016}, pages={447-456} }

We present a natural reverse Minkowski-type inequality for lattices, which gives upper bounds on the number of lattice points in a Euclidean ball in terms of sublattice determinants, and conjecture its optimal form. The conjecture exhibits a surprising wealth of connections to various areas in mathematics and computer science, including a conjecture motivated by integer programming by Kannan and Lovasz (Annals of Math. 1988), a question from additive combinatorics asked by Green, a question on… CONTINUE READING

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