Writing A GAP Package For Local Action Diagrams

Local action diagrams are a recent development which can be used to classify group
actions on a tree that are “(P)-closed”. Properties of local action diagrams are reflected in
the group acting on the tree. If a tree is locally finite and a (P)-closed group acting on it has
a finite number of orbits then the local action diagram associated with the group is finite,
which means a computer can use them to check for properties of the group. This project
aims to implement local action diagrams in the GAP computer algebra system, implement
functions that check for certain properties in them (and thus the group acting on the tree),
and also list representatives for all isomorphic local actions diagrams for a tree with a
given number of orbits.

Marcus Chijoff

The University of Newcastle

Marcus Chijoff is a student at The University of Newcastle studying Mathematics and Computer Science with majors in Pure Mathematics and Data Science. He plans to commence honors in Mathematics in 2023. He is most interested in using programming to help understand Mathematics.
Professionally, he has worked as a research assistant since 2020. During this time, he’s worked to develop a program to systematically search for novel examples of graphs satisfying certain properties. He has also been awarded two summer scholarships at The University of Newcastle. One studied linear error-correcting codes and the other studied the use of quaternionic wavelet transforms for colour image processing.

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