Lattice path coronoids

Author(s): Tricia Muldoon Brown1
1Department of Mathematical Sciences, Georgia Southern University, Savannah, GA, U.S.A.
Copyright © Tricia Muldoon Brown. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Coronoids are nice chemical structures that may be represented mathematically in the planar hexagonal lattice. They have been well-studied both for their chemical properties and also their enumerative aspects. Typical approaches to the latter type of questions often include classification and algorithmic techniques. Here we study one simple class of coronoids called hollow hexagons. Notably, hollow hexagons may be represented with a collection of partitions on the set \(\{2,3,4,6\}\). The hollow hexagons are used to classify another family of primitive coronoids, which we introduce here, called lattice path coronoids. Techniques from lattice path enumeration are used to count these newly-defined structures within equivalence classes indexed by enclosing hollow hexagons.

Keywords: Primitive coronoid; Lattice path; Partition.