Enumeration of 1-slab lattice links (Q2315305)

This paper studies the number of lattice links confined in \(1\)-slab, that is an \(m\times n \times 2\) cubic lattice. It provides generating functions for this class of lattice links with respect to the total length and the stick number of a lattice link as well as asymptotic analysis for the number of such lattice links. Note that this is not an enumeration of topologically different link types but an enumeration of combinatorially different sets of closed polygons in \(1\)-slab as it distinguishes lattice links by their shapes and locations. In other words, this paper studies the enumeration of sets of closed polygons in \(1\)-slab.