5 papers
Riesz and Green energy on projective spaces
Austin Anderson, Maria Dostert, Peter J. Grabner +2
In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projec…
Positive definiteness and the Stolarsky invariance principle
Dmitriy Bilyk, Ryan Matzke, Oleksandr Vlasiuk
In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a -invariant measure $μ…
Energy on spheres and discreteness of minimizing measures
Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke +2
In the present paper we study the minimization of energy integrals on the sphere with a focus on an interesting clustering phenomenon: for certain types of potentials, optimal meas…
The Maximum Size of -Sum-Free Sets in Cyclic Groups
Béla Bajnok, Ryan Matzke
A subset of a finite abelian group is called -sum-free if the sum of (not-necessarily-distinct) elements of never equals the sum of (not-necessarily-dist…
On the Fejes Tóth Problem about the Sum of Angles Between Lines
Dmitriy Bilyk, Ryan W Matzke
In 1959 Fejes Tóth posed a conjecture that the sum of pairwise non-obtuse angles between unit vectors in is maximized by periodically repeated elements of the sta…