How did Thomas Kirkman and Jakob Steiner contribute to combinatorial design theory?

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combinatorics Figure 1: Ferrers' partitioning diagram for 14.

Thomas Kirkman and Jakob Steiner are recognized for their foundational work in the development of design theory within the field of combinatorics.

In 1847, Thomas P. Kirkman began the study of triple systems, a specific area of combinatorial design. During the 1850s, Jakob Steiner, a Swiss-born German mathematician, further pursued this research. Their collective efforts in investigating these systems marked the formal beginning of the theory of design.1

While Kirkman is also noted for posing recreational problems—most famously the "Kirkman school girl problem"—his and Steiner's systematic exploration of triple systems provided the essential groundwork for the broader discipline of design theory.1