Poetry of Repetition: Constructing Verse through Combinatorial Design Theory
Ajani De Vas Gunasekara, Miriam Wei Wei Lo
TL;DR
This work addresses how combinatorial design theory can generate new poetic forms by employing Steiner triple systems ($STS(u)$) to impose structural constraints on word choices. The authors map poetry to graphs, showing that a Steiner triple poem on $u$ keywords is equivalent to a triangle decomposition of the complete graph $K_u$, with lines corresponding to edge-disjoint triangles and each pair of keywords appearing exactly once. They construct five poems using STS on seven and nine keywords, and illustrate pure, relaxed, and resolvable variants, supported by explicit graph representations of $K_7$ and $K_9$. The study reveals how mathematical structure can guide creative practice, producing a bidirectional dialog between mathematics and poetry and offering a blueprint for expanding mathematical forms into literary expression and education.
Abstract
This paper investigates the connections between combinatorial design theory and the creation of new forms of poetry through a specific combinatorial structure called Steiner triple systems. We introduce five original poems constructed using variations of Steiner triple systems on seven and nine words, illustrating how mathematical structures can inform and inspire new poetic forms. The work includes a reflective discussion from dual creative perspectives; one emphasizing structural design and the other, literary expression, highlighting how formal constraints can foster occasional frustrations, but also unexpected artistic freedoms. This study demonstrates the potential of mathematical frameworks as generative tools in literary creativity.