Tight Subdesigns of the Higman-Sims Design

Authors

Steven Klee, Valparaiso UniversityFollow
Leah Yates, East Carolina University

Abstract

The Higman-Sims design is an incidence structure of 176 points and 176 blocks of cardinality 50 with every two blocks meeting in 14 points. The automorphism group of this design is the Higman-Sims simple group. We demonstrate that the point set and the block set of the Higman-Sims design can be partitioned into subsets X1, X2,...,X11 and B1, B2,...,B11, respectively, so that the substructures (Xi, Bi), i = 1, 2,...,11, are isomorphic symmetric (16, 6, 2)-designs.

Author Bio

Steven Klee will be entering his final year at Valparaiso University in 2004. After graduation, he plans to enter a graduate program and pursue his PhD in mathematics. After that, he plans to obtain a teaching position at the university level where he will be able to lead research programs with undergraduate students. The research reported in this paper was done at the 2004 Central Michigan University Research Experience for Undergraduates with Leah Yates of East Carolina University, and under the guidance of Dr. Yury Ionin of Central Michigan University.

Faculty Sponsor

Yury J. Ionin

Recommended Citation

Klee, Steven and Yates, Leah (2004) "Tight Subdesigns of the Higman-Sims Design," Rose-Hulman Undergraduate Mathematics Journal: Vol. 5: Iss. 2, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol5/iss2/9