New Uniform Subregular Parallelisms of PG(3, 4) Invariant under an Automorphism of Order 2

Cybernetics and Information Technologies

Betten Anton¹  Zhelezova Svetlana²  Topalova Stela² 

[1] Colorado State University,Fort Collins, CO 80523 USA;Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113Sofia, Bulgaria;

关键词: finite geometry;    combinatorics;    classification;    isomorphism;    parallel computing;    spread;    parallelism;    mpi;   

DOI  :  10.2478/cait-2020-0057

来源: DOAJ

【 摘 要 】

A spread in PG(n, q) is a set of lines which partition the point set. A parallelism is a partition of the set of lines by spreads. A parallelism is uniform if all its spreads are isomorphic. Up to isomorphism, there are three spreads of PG(3, 4) – regular, subregular and aregular. Therefore, three types of uniform parallelisms are possible. In this work, we consider uniform parallelisms of PG(3, 4) which possess an automorphism of order 2. We establish that there are no regular parallelisms, and that there are 8253 nonisomorphic subregular parallelisms. Together with the parallelisms known before this work, this yields a total of 8623 known subregular parallelisms of PG(3, 4).

【 授权许可】

Unknown