34 citations · 53 across the 24 of their papers we have counts for
11 papers · 1 filter
On polynomial-time solvable linear Diophantine problems
Iskander Aliev
We obtain a polynomial-time algorithm that, given input (A, b), where A=(B|N) is an integer mxn matrix, m<n, with nonsingular mxm submatrix B and b is an m-dimensional integer vect…
Generalized Frobenius numbers: Bounds and average behavior
Iskander Aliev, Lenny Fukshansky, Martin Henk
We produce new upper and lower bounds for the s-Frobenius number by relating it to the so called s-covering radius of a certain convex body with respect to a certain lattice; this…
Expected Frobenius numbers
Iskander Aliev, Martin Henk, Aicke Hinrichs
We show that for large instances the order of magnitude of the expected Frobenius number is (up to a constant depending only on the dimension) given by its lower bound.
Integer Knapsacks: Average Behavior of the Frobenius Numbers
Iskander Aliev, Martin Henk
The main result of the paper shows that the asymptotic growth of the Frobenius number in average is significantly slower than the growth of the maximum Frobenius number.
Power maps and subvarieties of the complex algebraic --torus
Iskander Aliev, Chris Smyth
Given a subvariety of the complex algebraic torus defined by polynomials of total degree at most and a power map $ϕ: {\mathbb G}_{\rm m}^n \to {\mat…
Solving algebraic equations in roots of unity
Iskander Aliev, Chris Smyth
This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be describe…