Anosova, Olga and Kurlin, Vitaliy 
ORCID: 0000-0001-5328-5351
(2022)
Density functions of periodic sequences.
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Abstract
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.
| Item Type: | Conference or Workshop Item (Unspecified) |
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| Additional Information: | 12 pages, 4 figures, the latest version is at http://kurlin.org/projects/periodic-geometry-topology/densities1D.pdf. arXiv admin note: substantial text overlap with arXiv:2103.02749 |
| Uncontrolled Keywords: | cs.CG, cs.CG |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 29 Nov 2022 15:47 |
| Last Modified: | 18 Jan 2023 19:41 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3166413 |
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