7 citations · 22 across the 10 of their papers we have counts for
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math.CO2018★ 1 cited
On the number of integer points in translated and expanded polyhedra
Danny Nguyen, Igor Pak
We prove that the problem of minimizing the number of integer points inparallel translations of a rational convex polytope in is NP-hard. We apply this result to sho…
math.LO2018★ 2 cited
Presburger Arithmetic with algebraic scalar multiplications
Philipp Hieronymi, Danny Nguyen, Igor Pak
We consider Presburger arithmetic (PA) extended by scalar multiplication by an algebraic irrational number , and call this extension -Presburger arithmetic (-PA). We show…
math.LO2018
Parametric Presburger Arithmetic: Complexity of Counting and Quantifier Elimination
Tristram Bogart, John Goodrick, Danny Nguyen +1
We consider an expansion of Presburger arithmetic which allows multiplication by parameters . A formula in this language defines a parametric set $S_\mathbf{t}…