On the Enumeration of Shapes

Authors

May Cai, Georgia Institute of TechnologyFollow
Nicholas Liao, Georgia Institute of TechnologyFollow

Abstract

We define a shape as a union of finitely many line segments. Given an arrangement of lines on a plane, we count the number of shapes in the arrangement by examining the symmetries of the arrangement and applying Burnside's lemma. We further establish a generating function for the number of distinct line segments on a line with k distinguished points. We list all affine line arrangements of four and five line segments, together with the corresponding number of shapes on them.

Author Bio

May Cai graduated from the Georgia Institute of Technology in May 2018 with a Bachelor's degree in computer science. She is currently a PhD student at Georgia Tech.

Nicholas Liao graduated from the Georgia Institute of Technology in May 2018 with a Bachelor's degree in computer science. He currently works for Amazon Lab126.

Faculty Sponsor

Josephine Yu

Recommended Citation

Cai, May and Liao, Nicholas (2020) "On the Enumeration of Shapes," Rose-Hulman Undergraduate Mathematics Journal: Vol. 21: Iss. 1, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol21/iss1/3