# Density functions of periodic sequences

arXiv: https://arxiv.org/abs/2205.02226 · HTML: https://mlsanity.com/paper/2205.02226/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2022.

## Built on by (most cited first, 2 of 2)

- [Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives](https://mlsanity.com/paper/2303.15385/) (2023)
- [Blast Radius](https://mlsanity.com/paper/2608.07440/) (2026)

## Abstract (arXiv)

Periodic point sets model all solid crystalline materials whose structures are determined in a rigid form and should be studied up to rigid motion or isometry preserving inter-point distances. In 2021 H.Edelsbrunner et al. introduced an infinite sequence of density functions that are continuous isometry invariants of periodic point sets. These density functions turned out to be highly non-trivial even in dimension 1 for periodic sequences of points in the line. This paper fully describes the density functions of any periodic sequence and their symmetry properties. The explicit description theoretically confirms coincidences of density functions that were previously computed only through finite samples.