5 papers
On a new absolute version of Siegel's lemma
Maxwell Forst, Lenny Fukshansky
We establish a new version of Siegel's lemma over a number field , providing a bound on the maximum of heights of basis vectors of a subspace of , . In addition t…
On lattice extensions
Maxwell Forst, Lenny Fukshansky
A lattice is said to be an extension of a sublattice of smaller rank if is equal to the intersection of with the subspace spanned by . The goal of this paper is…
On zeros of multilinear polynomials
Maxwell Forst, Lenny Fukshansky
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove…
Counting basis extensions in a lattice
Maxwell Forst, Lenny Fukshansky
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by , producing an asym…
Positive Semidefiniteness of Matrices arising from Ramsey Theory
Joshua Cooper, Maxwell Forst
We resolve a conjecture of Cooper-Fenner-Purewal that a certain sequence of combinatorial matrices which can be used to bound small product-Ramsey numbers is positive semidefinite.…