A partial generalization of the Livingstone-Wagner Theorem

Yasuhiro Nakashima

Abstract


For a transitive permutation group G on a finite set Ω, the Livingstone–Wagner Theorem states that if G is k-homogeneous then G is (k − 1)-transitive. It can be conjectured that the number of G-orbits on k-subsets of Ω is greater than or equal to the one on ordered (k − 1)-tuples of Ω, if |Ω| is sufficiently large. For the simplest case k = 3, we prove this by establishing a result on edge-colorings of complete digraphs.

Keywords


Permutation group; Tranisitvity; Livingstone--Wagner Theorem

Full Text:

PDF ABSTRACTS (EN/SI)


DOI: https://doi.org/10.26493/1855-3974.92.46f

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications