Orbits on $k$-subsets of $2$-transitive Simple Lie-type Groups

Bradley, Paul; Rowley, Peter

doi:10.5802/alco.195

Orbits on

k

-subsets of

2

-transitive Simple Lie-type Groups

Bradley, Paul ¹; Rowley, Peter ²

¹ 31 Songthrush Way Norton Canes Cannock Staffordshire WS11 9AH UK
² Department of Mathematics University of Manchester Oxford Road Manchester M13 6PL UK

Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 37-51.

Abstract

For a finite rank one simple Lie-type group acting $2$ -transitively on a set $Ω$ and $k \in ℕ$ we derive formulae for the number of $G$ -orbits on the set of all $k$ -subsets of $Ω$ .

Received: 2020-10-03
Accepted: 2021-08-16
Revised after acceptance: 2021-08-18
Published online: 2022-02-28

DOI: 10.5802/alco.195

Classification: 20D06, 20B20
Keywords: Number of Orbits, $k$-subsets, rank one Lie-type groups.

Author's affiliations:

Bradley, Paul ¹; Rowley, Peter ²

¹ 31 Songthrush Way Norton Canes Cannock Staffordshire WS11 9AH UK
² Department of Mathematics University of Manchester Oxford Road Manchester M13 6PL UK

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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Bradley, Paul; Rowley, Peter. Orbits on $k$-subsets of $2$-transitive Simple Lie-type Groups. Algebraic Combinatorics, Volume 5 (2022) no. 1, pp. 37-51. doi : 10.5802/alco.195. https://alco.centre-mersenne.org/articles/10.5802/alco.195/

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