caa a22 4500 465825249 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112298 doi (NATIONALLICENCE)springer-10.1007/BF02112298 Resolvable Mendelsohn designs with block size 4 [Elektronische Daten] [F. Bennett, X. Zhang] Summary: Letv andK be positive integers. A (v, k, 1)-Mendelsohn design (briefly (v, k, 1)-MD) is a pair (X,B) whereX is av-set (ofpoints) andB is a collection of cyclically orderedk-subsets ofX (calledblocks) such that every ordered pair of points ofX are consecutive in exactly one block ofB. A necessary condition for the existence of a (v, k, 1)-MD isv(v−1) ≡ 0 (modk). If the blocks of a (v, k, 1)-MD can be partitioned into parallel classes each containingv/k blocks wherev ≡ ) (modk) or (v − 1)/k blocks wherev ≡ 1 (modk), then the design is calledresolvable and denoted briefly by (v, k, 1)-RMD. It is known that a (v, 3,1)-RMD exists if and only ifv ≡ 0 or 1 (mod 3) andv ≠ 6. In this paper, it is shown that the necessary condition for the existence of a (v, 4, 1)-RMD, namelyv ≡ 0 or 1 (mod 4), is also sufficient, except forv = 4 and possibly exceptingv = 12. These constructions are equivalent to a resolvable decomposition of the complete symmetric directed graphK v * onv vertices into 4-circuits. Birkhäuser Verlag, 1990 Primary 05B05 nationallicence Secondary 05C20 nationallicence Bennett F. Department of Mathematics, Mount Saint Vincent University, B3M 2J6, Halifax, Nova Scotia, Canada aut Zhang X. Department of Mathematics, Mount Saint Vincent University, B3M 2J6, Halifax, Nova Scotia, Canada aut aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 248-260 0001-9054 40:1<248 1990 40 10 https://doi.org/10.1007/BF02112298 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112298 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bennett F. Department of Mathematics, Mount Saint Vincent University, B3M 2J6, Halifax, Nova Scotia, Canada aut NATIONALLICENCE 700 1- Zhang X. Department of Mathematics, Mount Saint Vincent University, B3M 2J6, Halifax, Nova Scotia, Canada aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 248-260 0001-9054 40:1<248 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer