Some difference matrix constructions and an almost completion for the existence of triplewhist tournaments TWh(v)

Authors:
R. Julian R. Abel;Gennian Ge
Affiliations:
School of Mathematics, University of New South Wales, N.S.W., Australia;Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang, PR China
Venue:
European Journal of Combinatorics
Year:
2005

Citing 6
Cited 8

Design theory

Design theory
New product theorems for Z-cyclic whist tournaments

Journal of Combinatorial Theory Series A
Existence of Z-cyclic triplewhist tournaments for a prime number of players

Journal of Combinatorial Theory Series A
Perfect Cayley Designs as Generalizations of Perfect MendelsohnDesigns

Designs, Codes and Cryptography
Some new triplewhist tournaments TWh(v)

Journal of Combinatorial Theory Series A
A new construction for Z-cyclic whist tournaments

Discrete Applied Mathematics

Existence of Z-cyclic 3PTWh (p) for any Prime p≡ 1 (mod 4)

Designs, Codes and Cryptography
New Z-cyclic triplewhist frames and triplewhist tournament designs

Discrete Applied Mathematics
Existence of directedwhist tournaments with the three person property 3PDWh(v)

Discrete Applied Mathematics
General frame constructions for Z-cyclic triplewhist tournaments

Journal of Combinatorial Theory Series A
Existence of Z-cyclic 3PDTWh(p) for Prime p ≡ 1 (mod 4)

Designs, Codes and Cryptography
Triplewhist tournaments with the three person property

Journal of Combinatorial Theory Series A
Existence of directed triplewhist tournaments with the three person property 3PDTWh(v)

Discrete Applied Mathematics
Some 20-regular CDP(5,1;20u) and their applications

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

A necessary condition for the existence of a triplewhist tournament TWh(v) is v ≡ 0 or 1 (mod 4); this condition is known to be sufficient except for v = 5, 9, 12, 13 and possibly v = 17, 57, 65, 69, 77, 85, 93, 117, 129, 153. In this paper, we remove all the possible exceptions except v = 17. This provides an almost complete solution for the more than 100 year old problem on the existence of triplewhist tournaments TWh(v). By applying frame constructions and product constructions, several new infinite classes of Z-cyclic triplewhist tournaments are also obtained. A couple of new cyclic difference matrices are also obtained.