Add to ORKGInspired by Bárány’s colourful Carathéodory theorem [Bár82], we introduce a colourful generalization of Liu’s simplicial depth [Liu90]. We prove a parity property and conjecture that the minimum colourful simplicial depth of any core point in any d-dimensional configuration is d² + 1 and that the maximum is dd+1 + 1. We exhibit configurations attaining each of these depths, and apply our results to the problem of bounding monochrome (non-colourful) simplicial depth
Given a point p and d + 1 sets (i.e., colours) of points in dimension d, the Colourful Feasibility P...
Given $d+1$ sets of points, or colours, $\S_1,\ldots,\S_{d+1}$ in $\R^d$, a {\em colourful simplex} ...
Abstract. We consider set systems that satisfy a certain octa-hedral parity property. Such systems a...
Inspired by Bárány’s Colourful Carathéodory Theorem [4], we introduce a colourful generalization of ...
Abstract. The colourful simplicial depth conjecture states that any point in the convex hull of each...
The colourful simplicial depth conjecture states that any point in the convex hull of each of d+1 se...
ABSTRACT. The colourful simplicial depth conjecture states that any point in the convex hull of each...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
The colourful simplicial depth (CSD) of a point x in R^2 relative to a configuration P=(P^1, P^2, .....
The colourful simplicial depth conjecture states that any point in the convex hull of each of d+1 se...
We show that any point in the convex hull of each of (d+1) sets of (d+ 1) points in Rd is contained ...
We consider set systems that satisfy a certain octahe-dral parity property. Such systems arise when ...
Given a point p and d + 1 sets (i.e., colours) of points in dimension d, the Colourful Feasibility P...
Given $d+1$ sets of points, or colours, $\S_1,\ldots,\S_{d+1}$ in $\R^d$, a {\em colourful simplex} ...
Abstract. We consider set systems that satisfy a certain octa-hedral parity property. Such systems a...
Inspired by Bárány’s Colourful Carathéodory Theorem [4], we introduce a colourful generalization of ...
Abstract. The colourful simplicial depth conjecture states that any point in the convex hull of each...
The colourful simplicial depth conjecture states that any point in the convex hull of each of d+1 se...
ABSTRACT. The colourful simplicial depth conjecture states that any point in the convex hull of each...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
International audienceThe colourful simplicial depth conjecture states that any point in the convex ...
The colourful simplicial depth (CSD) of a point x in R^2 relative to a configuration P=(P^1, P^2, .....
The colourful simplicial depth conjecture states that any point in the convex hull of each of d+1 se...
We show that any point in the convex hull of each of (d+1) sets of (d+ 1) points in Rd is contained ...
We consider set systems that satisfy a certain octahe-dral parity property. Such systems arise when ...
Given a point p and d + 1 sets (i.e., colours) of points in dimension d, the Colourful Feasibility P...
Given $d+1$ sets of points, or colours, $\S_1,\ldots,\S_{d+1}$ in $\R^d$, a {\em colourful simplex} ...
Abstract. We consider set systems that satisfy a certain octa-hedral parity property. Such systems a...