Skip to main content

Research Repository

See what's under the surface


Orbits of primitive k-homogenous groups on (n-k)-partitions with applications to semigroups (2017)
Journal Article
Araújo, J., Bentz, W., & Cameron, P. J. (2018). Orbits of primitive k-homogenous groups on (n-k)-partitions with applications to semigroups. Transactions of the American Mathematical Society, 371, 105-136. https://doi.org/10.1090/tran/7274

The purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine the k-homogeneous permutation gro... Read More

Automorphism groups of circulant digraphs with applications to semigroup theory (2017)
Journal Article
Araújo, J., Bentz, W., Dobson, E., Konieczny, J., & Morris, J. (2018). Automorphism groups of circulant digraphs with applications to semigroup theory. Combinatorica, 38(1), 1-28. https://doi.org/10.1007/s00493-016-3403-0

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a "normal" ci... Read More