ICE-TCS seminar/UROP presentation: Eiður Sveinn Gunnarsson and Karl Þorláksson
Location, time and date: M122 at 1pm on Wednesday, 18 May.
Speakers: Eiður Sveinn Gunnarsson and Karl Þorláksson
Title: Generalized star polygons and polygrams
Abstract: We extend the definition of regular star polygons and other regular star polygrams to be drawn within some non self-intersecting polygon instead of just regular polygons. Instead of only connecting corners some constant apart, we allow any two corners of the polygon to be connected to form a figure. These figures can be thought of as permutations consisting of some cycles where each cycle forms a polygon. We define new permutation patterns called interacting cycle patterns that we use to describe properties of the permutations. We describe some necessary properties for a permutation drawn within a polygon, such that its drawing forms a star. Then we describe sufficient properties of permutations, such that when drawn within any available polygon they form stars.
Finally we describe sufficient properties of permutation drawings, that form a star in some polygon.