Open Journal of Discrete Applied Mathematics
Vol. 6 (2023), Issue 3, pp. 1 – 21
ISSN: 2617-9687 (Online) 2617-9679 (Print)
DOI: 10.30538/psrp-odam2023.0088
Lattice path coronoids
Tricia Muldoon Brown\(^{1,*}\)
\(^{1}\)Department of Mathematical Sciences, Georgia Southern University, Savannah, GA, U.S.A.; tmbrown@georgiasouthern.edu
Copyright © 2023 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.
Received: July 6, 2023 – Accepted: December 13, 2023 – Published: December 26, 2023
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.