<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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).</p></abstract>

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).

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

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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...

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

Published Online: Dec 31, 2020

Page range: 18 - 27

Received: Sep 15, 2020

Accepted: Oct 23, 2020

DOI: https://doi.org/10.2478/cait-2020-0057

Keywords
Finite Geometry, Combinatorics, Classification, Isomorphism, Parallel Computing, Spread, Parallelism, MPI

© 2020 Anton Betten et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Dec 31, 2020

Page range: 18 - 27

Received: Sep 15, 2020

Accepted: Oct 23, 2020

DOI: https://doi.org/10.2478/cait-2020-0057

KeywordsFinite Geometry, Combinatorics, Classification, Isomorphism, Parallel Computing, Spread, Parallelism, MPI

© 2020 Anton Betten et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Finite Geometry, Combinatorics, Classification, Isomorphism, Parallel Computing, Spread, Parallelism, MPI