Our investigations in the 1980's of Thue's method yielded determinants that we were only able to analyse successfully in part. We explain the context of our work, recount our experiences, mention our conjectures, and allude to a number of open questions.
"Determinants in the study of Thue's method and curves with prescribed singularities." Experiment. Math. 4 (2) 87 - 96, 1995.