MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Formal structure of periodic system of elements

Wilmer Leal and Guillermo Restrepo


For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is. Herein, based on the relations of order and similarity, we report a formal mathematical structure for the periodic system, which corresponds to an ordered hypergraph. It is shown that the current periodic system of chemical elements is an instance of the general structure. The definition is used to devise a tailored periodic system of polarizability of single covalent bonds, where order relationships are quantified within subsets of similar bonds and among these classes. The generalised periodic system allows envisioning periodic systems in other disciplines of science and humanities.

Feb 24, 2019
Feb 28, 2019
MSC Codes:
05C, 06F
Periodic System of Chemical Elements, Periodic Table, Ordered Hypergraph, Discrete models in Chemistry

Related publications

2019 Repository Open Access
Wilmer Leal and Guillermo Restrepo

Formal structure of periodic system of elements

In: Proceedings of the Royal Society of London / A, 475 (2019) 2224, p. 20180581