15 citations · 18 across the 4 of their papers we have counts for
8 papers
On the area of empty axis-parallel rectangles amidst 2-dimensional lattice points
Thomas Lachmann, Jaspar Wiart
The dispersion of a point set in the unit square is defined to be the area of the largest empty axis-parallel box. In this paper we are interested in the dispersion of lattices in…
The VC-Dimension of Axis-Parallel Boxes on the Torus
Pierre Gillibert, Thomas Lachmann, Clemens Müllner
We show in this paper that the VC-dimension of the family of -dimensional axis-parallel boxes and cubes on the -dimensional torus are both asymptotically . This…
On the number of gaps of sequences with Poissonian Pair Correlations
Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti +1
A sequence on the torus is said to have Poissonian pair correlations if for all reals , as . It…
Geometric Generalization Based Zero-Shot Learning Dataset Infinite World: Simple Yet Powerful
Rajesh Chidambaram, Michael Kampffmeyer, Willie Neiswanger +3
Raven's Progressive Matrices are one of the widely used tests in evaluating the human test taker's fluid intelligence. Analogously, this paper introduces geometric generalization b…
The Duffin-Schaeffer conjecture with extra divergence
Christoph Aistleitner, Thomas Lachmann, Marc Munsch +2
The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. It asserts that for every non-negative function fo…
There is no Khintchine threshold for metric pair correlations
Christoph Aistleitner, Thomas Lachmann, Niclas Technau
We consider sequences of the form mod 1, where and where is a strictly increasing sequence of positive in…