SURVEY ON ISLANDS – a possible research topic, even for students

In recent algebra investigations, the maximum number of islands on some grid turned out to appear as interesting combinatorial problem. The aim of this paper is to overview the history and the results in this topic. The first result, the formula of Gábor Czédli appeared in [2], his proof was based on lattice theory. The investigation went on two different directions, nowadays both are living research areas. 1. Lattice theory direction: After discovering the relationship between the maximum number of rectangular islands and the weak bases of finite distributive lattices, new investigations and new results appeared within lattice theory. 2. Elementary direction: After discovering two elementary proof techniques in [1], several new questions and answers have been born, some of which can be asked and answered even by high-school level knowledge. We are convinced that these theoretical investigations will interact each other in the future, providing further results and applications as well. There are already many easily understandable open problems in this topic, giving challenge to the researching mathematicians (as well as to the students). We would like to introduce the topic the reader, in order to study it further by choosing some paper from the References.