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No 17‐player triplewhist tournament has nontrivial automorphisms
Author(s) -
Haanpää Harri
Publication year - 2005
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/jcd.20038
Subject(s) - tournament , automorphism , mathematics , automorphism group , combinatorics , group (periodic table) , physics , quantum mechanics
The existence of triplewhist tournaments for v players has recently been solved for all values of v except = 17. For v = 12 and v = 13, a complete enumeration has shown the nonexistence of TWh ( v ), while constructions of TWh ( v ) have been presented for v > 17. For several values of v , existence has been shown by constructing a TWh ( v ) with a prescribed, usually cyclic, automorphism group. In this article, it is shown that the strategy of constructing a TWh ( v ) with a prescribed automorphism group cannot succeed with TWh (17), since no 17‐player triplewhist tournament has nontrivial automorphisms. © 2004 Wiley Periodicals, Inc.