Towards Strong Reverse Minkowski-Type Inequalities for Lattices

  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)},
  • Daniel Dadush, Oded Regev
  • Published in
    IEEE 57th Annual Symposium on…
  • Mathematics, Computer Science
  • 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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