| Title: | Polycyclic geometric realizations of the Gray configuration |
|---|
| Authors: | ID Berman, Leah (Author)
ID Gévay, Gábor (Author)
ID Pisanski, Tomaž (Author) |
|---|
| Files: |  RAZ_Berman_Leah_2025.pdf (2,95 MB)
MD5: EBD721C3CAAF3B74E0EDDB6B2ABA3962
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
IAM - Andrej Marušič Institute
|
|---|
| Abstract: | The Gray configuration is a (27_3) configuration which typically is realized as the points and lines of the 3×3×3 integer lattice. It occurs as a member of an infinite family of configurations defined by Bouwer in 1972. Since their discovery, both the Gray configuration and its Levi graph (i.e., its point-line incidence graph) have been the subject of intensive study. Its automorphism group contains cyclic subgroups isomorphic to Z3 and Z9, so it is natural to ask whether the Gray configuration can be realized in the plane with any of the corresponding rotational symmetry. In this paper, we show that there are two distinct polycyclic realizations with Z3 symmetry. In contrast, the only geometric polycyclic realization with straight lines and Z9 symmetry is only a “weak” realization, with extra unwanted incidences (in particular, the realization is actually a (27_4) configuration). |
|---|
| Keywords: | Gray graph, Gray configuration, polycirculant, polycyclic configuration |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 26.09.2025 |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | str. 171-197 |
|---|
| Numbering: | Vol. 93, pt. 1 |
|---|
| PID: | 20.500.12556/RUP-21805  |
|---|
| UDC: | 51 |
|---|
| ISSN on article: | 2202-3518 |
|---|
| COBISS.SI-ID: | 250814979 |
|---|
| Publication date in RUP: | 29.09.2025 |
|---|
| Views: | 420 |
|---|
| Downloads: | 4 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
