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On Minkowski space and finite geometry
Orel, Marko, matematik, 1980-
Poglavitni cilj tega interdisciplinarnega članka je klasifikacija vseh preslikav na končnem analogu prostora Minkowskega poljubne dimenzije ▫$n$▫, ki slikajo pare različnih dogodkov svetlobnega tipa ...v pare različnih dogodkov svetlobnega tipa. Pri tem ni privzeta niti bijektivnost preslikav niti ohranjanje omenjene lastnosti v obratni smeri, tj. iz kodomene v domeno. Popolna klasifikacija je podana v mnogih primerih, ki vključujejo dimenzije ▫$n$▫, ki so deljive s 4 ter lihe dimezije ▫$\geq 9$▫. V splošnem je pokazano, da je obstoj tovrstnih preslikav, ki niso bijektivne, neposredno povezan z obstojem ovoidov v ortogonalnem polarnem prostoru, kar predstavlja pomemben problem v končni geometriji. Slednji je odprt že nekaj desetletij kljub številnim raziskavam na tem področju. Dokazi temeljijo na preučevanju jedra afinega polarnega grafa, kar med drugim privede do sorodnih rezultatov, kot sta jih pred tem za točkovni graf polarnega prostora dognala Cameron in Kazanidis (2008).
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