Introducing a unified magnetic space-group symbol

This article introduces a `unified' (UNI) magnetic space-group symbol.

Irreducible and site-symmetry-induced representations of single/double ordinary/grey layer groups

For single and double, ordinary and grey layer groups G, all the irreducible (half-)integer (co-)representations D^(μ)(G) are derived as well as the allowed (co-)representations of the little groups. Band representations for all types of layer groups are induced from the irreducible representations of the site-symmetry groups and decomposed into the irreducible components. Together with many other important characteristics of the layer groups, these results are derived with the program code POLSym and presented at the new web site https://nanolab.group/layer/.

Combinatorial aspects of the Löwenstein avoidance rule. Part II: local and global constraints

Local and global constraints mostly determine the value of independence ratios of 2-periodic nets.

Tangled piecewise-linear embeddings of trivalent graphs

Embeddings of tangled trivalent graphs, with linear connectors (or `sticks') between vertices, are generated under appropriate point-group symmetries, and described. These structures present interesting targets for molecular synthesis of tangled molecules.

A simplified relationship between the modified O-lattice and the rotation matrix for generating the coincidence site lattice of an arbitrary Bravais lattice system

A simplified relationship between the modified O-lattice and the rotation matrix of any Bravais lattice was established for the generation of a coincidence site lattice wherever it exists.

On the combinatorics of crystal structures: number of Wyckoff sequences of given length

A formula for the calculation of the number of Wyckoff sequences of a given space-group type and length is presented, and applied to make a comparison between the calculated frequencies of occurrence of Wyckoff sequences and those observed in the Pearson's Crystal Data Crystal Structure Database for Inorganic Compounds.

Coordination sequences of periodic structures are rational via automata theory

The conjecture of Grosse-Kunstleve et al., that coordination sequences of periodic structures in n-dimensional Euclidean space are rational, is proved. This has been recently proven by Nakamura et al.; however, the proof presented here is a straightforward application of classic techniques from automata theory.