Affiliation:
1. Vladimir State University
2. Lomonosov Moscow State University
3. Kola Science Centre of RAS
Abstract
Lattice partitions of a plane into polyominoes were constructed for N from 3 to 12, where N is the order of the packing space. We obtained 5191 symmetric independent lattice partitions of a plane with one polyomino in a reduced (primitive) cell, among which 122 variants belong to the structural class cm, Z = 2(m), with the elementary conventional cell being rectangular (centered). Chain partitions of planes have been derived, for which both structural class and structural subclass were identified. The results of the analysis of lattice partitions of a plane into polyominoes were illustrated with examples of real molecular layers in crystal structures.