Premium
Cyclic antiautomorphisms of directed triple systems
Author(s) -
Carnes Neil P.,
Dye Anne,
Reed James F.
Publication year - 1996
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1996)4:2<105::aid-jcd3>3.0.co;2-j
Subject(s) - combinatorics , mathematics , triple system , transitive relation , permutation (music) , order (exchange) , pairwise comparison , fixed point , set (abstract data type) , discrete mathematics , pure mathematics , computer science , physics , mathematical analysis , statistics , finance , acoustics , economics , programming language
A transitive triple, ( a , b , c ), is defined to be the set {( a , b ), ( b , c ), ( a , c )} of ordered pairs. A directed triple system of order v , DTS( v ), is a pair ( D ,β), where D is a set of v points and β is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of β. An antiautomorphism of a Directed triple system, ( D ,β), is a permutation of D that maps β to β −1 , where β −1 = {( c , b , a )|( a , b , c ) E β}. In this article we give necessary and sufficient conditions for the existence of a Directed triple system of order v admitting an antiautomorphism consisting of a single cycle of length d and having v − d fixed points. Further, we give a more general result for partial Directed triple systems in which the missing ordered pairs are precisely those containing two fixed points. © 1996 John Wiley & Sons, Inc.