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math.CA2022★ 5 cited
Infinite constant gap length trees in products of thick Cantor sets
Alex McDonald, Krystal Taylor
We show that products of sufficiently thick Cantor sets generate trees in the plane with constant distance between adjacent vertices. Moreover, we prove that the set of choices for…
math.CA2022
Nonempty interior of configuration sets via microlocal partition optimization
Allan Greenleaf, Alex Iosevich, Krystal Taylor
We prove new results of Mattila-Sjölin type, giving lower bounds on Hausdorff dimensions of thin sets ensuring that various -point configuration sets, genera…
math.CA2022
Lattice Points Close to the Heisenberg Spheres
Elizabeth Campolongo, Krystal Taylor
We study a lattice point counting problem for spheres arising from the Heisenberg groups. In particular, we prove an upper bound on the number of points on and near large dilates o…