36 citations · 170 across the 43 of their papers we have counts for
10 papers · 1 filter
Space vectors forming rational angles
Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen +1
We classify all sets of nonzero vectors in such that the angle formed by each pair is a rational multiple of . The special case of four-element subsets lets us cl…
Semidefinite programming bounds for the average kissing number
Maria Dostert, Alexander Kolpakov, Fernando Mário de Oliveira Filho
The average kissing number of is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in . We provid…
Kissing number in spherical space
Maria Dostert, Alexander Kolpakov
This paper investigates the behaviour of the kissing number of congruent radius spheres in , for . Such a quantity depends on the radius $r…
Kissing number in hyperbolic space
Maria Dostert, Alexander Kolpakov
This paper provides upper and lower bounds on the kissing number of congruent radius spheres in , for . For that purpose, the kissing number is repla…
Spherical tetrahedra with rational volume, and spherical Pythagorean triples
Alexander Kolpakov, Sinai Robins
We study spherical tetrahedra with rational dihedral angles and rational volumes. Such tetrahedra occur in the Rational Simplex Conjecture by Cheeger and Simons, and we supply vast…
The dual Jacobian of a generalised tetrahedron, and volumes of prisms
Alexander Kolpakov, Jun Murakami
We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron.…