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On graphical designs
Abstract
A fundamental question in the theory of combinatorial designs is to ask what designs can be obtained with a particular automorphism group. This work completely determines all proper Steiner graphical t-wise balanced designs that have the group $S\sb{n}\ wr\ S\sb{r}$ (wreath product) acting on the set of $n\sp2(\sbsp{2}{r})$ edges of the complete r-partite graph, $K\sb{n,n,{\...},n}$, except when r = 3. The cases $n = 1,\ r \ge 2$ and $n \ge 2,\ r = 2$ were previously determined. The only proper Steiner graphical t-wise balanced designs that occur are given in Table I, with the possible exception of some more designs when r = 3. A major portion of the classification required descent arguments that reduced larger parameter situations to smaller ones.
Subject Area
Mathematics
Recommended Citation
Olsen, Cheryl L, "On graphical designs" (1997). ETD collection for University of Nebraska-Lincoln. AAI9734631.
https://digitalcommons.unl.edu/dissertations/AAI9734631