A Combinatorial Problem from Group Theory

Eugene Curtin, Suho Oh

Published 2017-01-30Version 1

Keller proposed a combinatorial conjecture on construction of an n-by-infinite matrix, which comes from showing the existence of many orbits of different sizes in certain linear group actions. He proved it for the case n=4, and we show that conjecture is true in the general case. We also propose a combinatorial game version of the conjecture which even further generalizes the problem.