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On The Enumeration Of Shapes, May Cai, Nicholas Liao
On The Enumeration Of Shapes, May Cai, Nicholas Liao
Rose-Hulman Undergraduate Mathematics Journal
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.