20.500.12556/RUP-21805 Polycyclic geometric realizations of the Gray configuration 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). Gray graph Gray configuration polycirculant polycyclic configuration Grayev graf Grayeva konfiguracija policirkulant policiklična konfiguracija true false true Angleški jezik Slovenski jezik Članek v reviji 2025-09-29 10:27:55 2025-09-29 10:27:56 2025-10-17 03:05:21 0000-00-00 00:00:00 2025 0 0 str. 171-197 pt. 1 Vol. 93 2025 0000-00-00 Zaloznikova NiDoloceno NiDoloceno 0000-00-00 0000-00-00 2025-09-26 51 2202-3518 250814979 RAZ_Berman_Leah_2025.pdf RAZ_Berman_Leah_2025.pdf 1 EBD721C3CAAF3B74E0EDDB6B2ABA3962 3c9c5e3e149c004c84b1f3be57804ceb45ce5c7da209e9b69830e22ba0be99a1 5de17a49-9d0e-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31711 Fakulteta za matematiko, naravoslovje in informacijske tehnologije Inštitut Andrej Marušič 0 0 0