Enumeration of 1-slab lattice links

Lattice knot statistics which is the study of knotted polygons in the simple cubic lattice have been deeply studied. In this paper, we discuss the enumeration of lattice links and fully-packed lattice links confined to slabs of width 1, as a model for multi-component ring polymers in physics. Moreover, the generating functions for such 1-slab lattice links with respect to the total length and the number of sticks are determined. We also analyze the asymptotic behavior of the growth rates of their cardinality.