Intersection Cographs and Aesthetics

Journal of Humanistic Mathematics

article

Haas, Robert¹ 

[1] Cleveland Heights

关键词: art;    finite geometry;    graph labeling;    graph theory;    literature;    mathematical model;    music;    poetry;   

DOI  :  10.5642/jhummath.202201.03

学科分类：社会科学、人文和艺术（综合）

来源: Claremont Center for the Mathematical Sciences

【 摘 要 】

Cographs are complete graphs with colored lines (edges); in an intersection cograph, the points (vertices) and lines (edges) are labeled by sets, and the line between each pair of points is (or represents) their intersection. This article first presents the elementary theory of intersection cographs: 15 are possible on 4 points; constraints on the triangles and quadrilaterals; some forbidden configurations; and how, under suitable constraints, to generate the points from the lines alone. The mathematical theory is then applied to aesthetics, using set cographs to describe the experience of a person enjoying a picture (Mu Qi), poem (Dickinson), play (Shakespeare), or piece of music (Anna Magdalena Bach).

【 授权许可】

CC BY-NC-ND