4 citations · 8 across the 23 of their papers we have counts for
26 papers
Integer triangles with a rational ratio of circumcircle radius to excircle radius
Lorenz Halbeisen, Norbert Hungerbühler, Arman Shamsi Zargar
We consider the problem of finding integer triangles with a positive rational, where and are the radii of the circumcircle and an excircle, respectively. We show that…
There may be exactly -points
Lorenz Halbeisen, Silvan Horvath, Tan Özalp
We generalize the main result of arXiv:2505.17960 and show the consistency of the statement ``There are exactly -points up to isomorphism" for any finite . Furthermore, w…
A unique -point and infinitely many near-coherence classes of ultrafilters
Lorenz Halbeisen, Silvan Horvath, Saharon Shelah
We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length- countable support iteration of restricted Mathias forcing over a groun…
Pairing Powers of Pythagorean Pairs
Lorenz Halbeisen, Norbert Hungerbühler, Arman Shamsi Zargar
A pair of positive integers is a pythagorean pair if is a square. A pythagorean pair is called a pythapotent pair of degree if there is another py…
Properties of Hesse derivatives of cubic curves
Sayan Dutta, Lorenz Halbeisen, Norbert Hungerbühler
The Hesse curve or Hesse derivative Hess of a cubic curve given by a homogeneous polynomial is the set of points such that , whe…
Implications of Ramsey Choice Principles in ZF
Lorenz Halbeisen, Riccardo Plati, Saharon Shelah
The Ramsey Choice principle for families of -element sets, denoted , states that every infinite set has an infinite subset with a choice functi…