# Advances in Z -cyclic whist and triplewhist tournaments

#### Abstract

While the existence of whist tournaments on 4*n* and 4* n* + 1 players is known for all *n* ≥ 1, the existence, and subsequently the construction, for Z-cyclic whist and Z-cyclic triplewhist tournaments on 4*n* and 4*n* + 1 players are not known for all *n* ≥ 1. In this study, existence theorems and constructions will be sought for (1) Z-cyclic triplewhist tournaments on 3*qp ^{n}* players where q∈7,11 ,

*p*is a prime less than 2000,

*p*≡ 1 (mod 4) and

*n*is a positive integer. (2) Z-cyclic triplewhist tournaments on 3

*qp*

_{1}

*p*

_{ 2}and 3

*qp*

_{1}

*p*

_{2}

*p*

_{3}players where q∈7,11 and pi∈5,13,17 for

*i*= 1, 2, 3. (3) Z-cyclic whist tournaments on 3

^{3}

*p*

_{1}+ 1 and 3

^{3}

*p*

_{1}

*p*

_{2}+ 1 players where

*p*is a prime,

_{i}*p*≡ 1 (mod 4) and gcd(18,

_{i}*p*− 1) = 18 for

_{i}*i*= 1, 2.^

#### Subject Area

Mathematics

#### Recommended Citation

Adele Johanna Josiger Merritt,
"Advances in Z -cyclic whist and triplewhist tournaments"
(1999).
*Dissertations and Master's Theses (Campus Access).*
Paper AAI9945216.

http://digitalcommons.uri.edu/dissertations/AAI9945216