345 papers
This paper investigates the plane geometry of -rationals by constructing deformed Farey triangulations and modular surfaces, interpreting these numbers as Ford-like circles, and introducing Springborn operations as quadratic generalizations of Farey addition that correspond geometrically to the homothety centers of circle pairs.
This paper demonstrates that for Kautz graphs with sufficiently large diameters, a regular routing scheme achieves a better all-to-all makespan than any shortest-path routing scheme by proving the existence of edges with congestion strictly exceeding the regular routing's step count.
This paper generalizes Backhausz and Szegedy's result on the infinite regular tree by proving that the Gaussian wave is the unique typical process with Green's function covariance for any infinite tree of finite cone type satisfying mild expansion, thereby establishing the convergence of local eigenvector distributions to the Gaussian wave for random bipartite biregular graphs and generic configuration models.
This paper introduces the concept of abelian-normal numbers by adapting abelian complexity functions to digit expansions, constructs a non-normal analogue of Champernowne's constant that satisfies this new property, and proposes open problems regarding its behavior.
This paper demonstrates that while the classical problem of Euler's thirty-six officers has no solution for order six, a solution exists using entangled quantum Latin squares, whereas mutually orthogonal quantum Latin squares of order six are impossible without entanglement.