For a transitive permutation group ?$G$? on a finite set ?$\Omega$?, the Livingstone-Wagner Theorem states that if ?$G$? is ?$k$?-homogeneous and ?$2 \le k \le \frac{\vert \Omega \vert}{2}$?, then ?$G$? is ?$(k - 1)$?-transitive. We conjecture that the number of ?$G$?-orbits on ?$k$?-subsets of ?$\Omega$? is greater than or equal to the number of ?$G$?-orbits on ordered ?$(k - 1)$?-tuples of ?$\Omega$?, if ?$\vert \Omega \vert$? is sufficiently large. For the simplest case ?$k = 3$?, we verify this conjecture by establishing a result on edge-colorings of complete digraphs.

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URN

URN:NBN:SI:DOC-OX8GNVQV

COBISSID

15498585

Added

16.12.2021

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Citation

APA:

Nakashima, Yasuhiro (2009). A partial generalization of the Livingstone-Wagner Theorem. Ars mathematica contemporanea, volume 2, issue 2, str. 207-215. URN:NBN:SI:DOC-OX8GNVQV from http://www.dlib.si

MLA:

Nakashima, Yasuhiro. "A partial generalization of the Livingstone-Wagner Theorem." Ars mathematica contemporanea volume 2. issue 2 (2009) str. 207-215.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-OX8GNVQV>

Ars mathematica contemporanea
2008-
(Assembly record)