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We study a variant of the ErdH os unit distance problem, concerning angles between successive triples of points chosen from a large finite point set. Specifically, given a large finite set of $n$ points $E$, and a sequence of angles $(alpha_1,ldots,alpha_k)$, we give upper and lower bounds on the maximum possible number of tuples of distinct points $(x_1,dots, x_{k+2})in E^{k+2}$ satisfying $angle (x_j,x_{j+1},x_{j+2})=alpha_j$ for every $1le j le k$ as well as pinned analogues.
The ErdH{o}s distinct distance problem is a ubiquitous problem in discrete geometry. Less well known is ErdH{o}s distinct angle problem, the problem of finding the minimum number of distinct angles between $n$ non-collinear points in the plane. The s
Interior and exterior angle vectors of polytopes capture curvature information at faces of all dimensions and can be seen as metric variants of $f$-vectors. In this context, Grams relation takes the place of the Euler-Poincare relation as the unique
We study variants of Mastermind, a popular board game in which the objective is sequence reconstruction. In this two-player game, the so-called textit{codemaker} constructs a hidden sequence $H = (h_1, h_2, ldots, h_n)$ of colors selected from an alp
In this paper we initiate the study of tropical Voronoi diagrams. We start out with investigating bisectors of finitely many points with respect to arbitrary polyhedral norms. For this more general scenario we show that bisectors of three points are
A classic theorem of Euclidean geometry asserts that any noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chvatal conjectured that this holds for an arbitrary finite metric space, with a certain natural def