Extended directed triple systems with a given automorphism
Commun. Korean Math. Soc. 2004 Vol. 19, No. 2, 355-373
Printed June 1, 2004
Chung Je Cho, Yong-Hyeon Han
Sookmyung Women's University, Sookmyung Women's University
Abstract : An {\it extended directed triple system of order $v$\/}, denoted by $EDTS(v)$, is a pair $(V,\frak B)$ where $V$ is a $v$-set and $\frak B$ is a set of transitive triples of elements of $V$ such that every ordered pair of elements of $V$ is contained in exactly one member of $\frak B$. We obtain a necessary and sufficient condition for the existence of cyclic $EDTS(v)$s, and when $k=1$ or 2, we also obtain a necessary and sufficient condition for the existence of $k$-rotational $EDTS(v)$s.
Keywords : extended directed triple system, automorphism
MSC numbers : 05B05, 05B07, 05B10
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