A bar 1-visibility drawing of a graph G is a drawing of G where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment where the vertical line segment representing an edge must connect the horizontal line segments representing the end vertices and a vertical line segment corresponding to an edge intersects at most one bar which is not an en...

Periodic series of period T can be mapped into the set permutations [T−1]={1,2,3,…,T−1}. These classified according to relative ordering their elements by horizontal visibility map. We prove that number classes for each coincides with triangulations polygon T+1 vertices that, as is well known, Catalan CT−1. also study robustness against Gaussian noise permutation patterns and show there are per...

We study the distributional properties of horizontal visibility graphs associated with random restrictive growth sequences and set partitions size n. Our main results are formulas expressing expected degree graph nodes in terms simple explicit functions a finite collection Stirling Bernoulli numbers.

A visibility drawing of a plane graph G is a drawing of G where each vertex is drawn as a horizontal line segment and each edge is drawn as a vertical line segment such that the line segments use only grid points as their endpoints. The area of a visibility drawing is the area of the smallest rectangle on the grid which encloses the drawing. A minimum-area visibility drawing of a plane graph G ...

Die selbständige und eigenhändige Anfertigung versichere ich an Eides statt. Conclusion 71 Bibliography 75 Introduction " The true mystery of the world is the visible, not the invisible. " Oscar Wilde How can geometric settings be encoded combinatorially? Which discrete structures extract the essential information from continuous arrangements? How can the combinatorial properties of visibility ...

Orientation perception is known to be anisotropic, with cardinal axes (i.e., horizontal and vertical) being privileged. Indeed, orientation sensitivity is greater near the cardinals, and small deviations from cardinal axes may be illusorily perceived in an exaggerated manner. Here, we quantified this illusory deviation from the cardinals at various visibility levels, by having participants repr...

A bar visibility representation of a graph G is a collection of horizontal bars in the plane corresponding to the vertices of G such that two vertices are adjacent if and only if the corresponding bars can be joined by an unobstructed vertical line segment. In a bar k-visibility graph, two vertices are adjacent if and only if the corresponding bars can be joined by a vertical line segment that ...