• Communications of the Korean Mathematical Society
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• v.16 no.2
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• pp.309-317
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• 2001

A directed triple system of order ν, denoted by DTS(ν), is said to be $textsc{k}$-near rotational if it admits an automorphism consisting of exactly three fixed elements and $textsc{k}$ cycles of length (ν-3)/$textsc{k}$. In this paper, we obtain necessary and sufficient conditions for the existence of $textsc{k}$-near rotational DTS(ν)s for every positive integer $textsc{k}$.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.231-239
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• 2008

We obtain a necessary and sufficient condition for the existence of Mendelsohn triple systems excluding contiguous units with ${\lambda}$ = 1. Also, we obtain the spectrum for cyclic such systems.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.355-373
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• 2004

An extended directed triple system of order v, denoted by EDTS(v), is a pair (V, (equation omitted)) where V is a v-set and (equation omitted) 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 (equation omitted). 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.