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Some new Z-cyclic whist tournament designs

Ian Anderson, Norman J. Finizio
2005 Discrete Mathematics  
Several other new infinite classes of Z-cyclic whist tournaments are also obtained.  ...  Moore, in his seminal work on whist tournaments, provided a construction that yields Z-cyclic whist designs on 3p + 1 players for every prime p of the form p = 4n + 1.  ...  A whist tournament on v players is denoted by Wh(v). Each (near) resolution class of the design is called a round of the tournament.  ... 
doi:10.1016/j.disc.2004.08.019 fatcat:ymediekcx5hvzjnxymn3hzyjwm

Directed–ordered whist tournaments and (v,5,1) difference families: existence results and some new classes of Z-cyclic solutions

R. Julian, R. Abel, Stephanie Costa, Norman J. Finizio
2004 Discrete Applied Mathematics  
In addition many new examples of Z-cyclic directed whist tournaments and ordered whist tournaments are given.  ...  Several new (v; 5; 1) di erence families are given and are combined with a construction of Buratti and Zuanni to produce Z-cyclic directed-ordered whist tournaments.  ...  The DFs here include both some unpublished cases mentioned in [1] and some new designs. We classify these DFs into three di erent types.  ... 
doi:10.1016/j.dam.2003.12.005 fatcat:nar7p7gisjbnfpyjj2sd4xcj2q

Page 8404 of Mathematical Reviews Vol. , Issue 2000m [page]

2000 Mathematical Reviews  
Key (1-CLEM; Clemson, SC) 2000m:05052 05B30 Finizio, Norman J. (1-RI; Kingston, RI); Merritt, Adele J. (1-RI; Kingston, RI) Some new Z-cyclic whist tournaments. (English summary) Discrete Appl.  ...  Ian Anderson (4-GLAS; Glasgow) 2000m:05053 05B30 Finizio, Norman J. (1-RI; Kingston, RD); Merritt, Adele J. (1-RI; Kingston, RI) Extensions of some Z-cyclic whist tournaments.  ... 

General frame constructions for Z-cyclic triplewhist tournaments

Gennian Ge
2007 Journal of combinatorial theory. Series A  
As an application, some new Z-cyclic triplewhist tournament frames and Z-cyclic triplewhist tournaments are obtained. The known existence results of such designs are then extended. Example 4.3.  ...  Z-cyclic triplewhist tournament frames are also useful in the constructions of Z-cyclic triplewhist tournaments.  ...  As an application, some new Z-cyclic triplewhist tournament frames and Z-cyclic triplewhist tournaments are obtained. The known existence results of such designs are then extended.  ... 
doi:10.1016/j.jcta.2006.08.011 fatcat:pf5jak7np5cx7m34qifh6cgjqm

Classification of whist tournaments with up to 12 players

Harri Haanpää, Patric R.J. Östergård
2003 Discrete Applied Mathematics  
Directed whist tournaments DWh(v), and triplewhist tournaments TWh(v), are Wh(v) with certain additional requirements.  ...  A v-player whist tournament Wh(v) is a schedule of games, each involving two players opposing two others. Every round, the players are partitioned into games, with at most one player left over.  ...  Petteri Kaski is also acknowledged for providing us with the resolved (12; 4; 3)-designs computed in [10] .  ... 
doi:10.1016/s0166-218x(02)00578-4 fatcat:k2bxwxlodrbodkwqkhphezv6de

A new construction for Z-cyclic whist tournaments

Gennian Ge, Alan C.H. Ling
2003 Discrete Applied Mathematics  
In this paper, a new construction for Z-cyclic whist tournaments is given. The known existence results for both Z-cyclic whist tournaments and Z-cyclic triplewhist tournaments are extended. ?  ...  Since a homogeneous (q; 4; 1)-CDM exists from Lemma 3.3 and a Z-cyclic TWh(q+1) exists from Theorem 1.2, we may apply the product construction of Theorem 3.9 to obtain a Z-cyclic TWh(qv + 1).  ...  To prove the third assertion, we start with a Z-cyclic TWh(v) constructed as above.  ... 
doi:10.1016/s0166-218x(03)00381-0 fatcat:gpwfq3uqufadhej4soct42qou4

Z-cyclic generalized whist frames and Z-cyclic generalized whist tournaments

Norman J Finizio, Brian J Travers
2004 Discrete Mathematics  
We extend their ideas to generalized whist tournament designs. Thus, in one sense, we provide a complete generalization of their methodology.  ...  Our techniques are illustrated by the production of many new Z-cyclic (2,6) GWhD(v) that would be di cult to produce by any other existing method.  ...  Some new Z -cyclic (2; 6)GWhD(v) In this section we combine materials from Sections 1-3 to obtain some new Z-cyclic (2; 6)GWhD(v). For reference we list some designs that appear in [4] . Example 24.  ... 
doi:10.1016/s0012-365x(03)00271-1 fatcat:ks7py2dzfngjdjbkx5njkkdfli

On (g,4;1)-difference matrices

Gennian Ge
2005 Discrete Mathematics  
Some new results on (g, k; 1)-CDMs are also obtained, which are useful in the construction of both optical orthogonal codes and Z-cyclic whist tournaments.  ...  If G = Z g , the difference matrix is called cyclic and denoted by (g, k; 1)-CDM. Motivated by the construction of g-fan H(4, g, 4, 3), we consider the existence of (g, 4; 1)-DMs.  ...  If there exists a Z-cyclic triplewhist or directed whist tournament W h(v), then there exists a (v, 5; 1)-CDM. Proof. Suppose we have a Z-cyclic triplewhist tournament W h(v) .  ... 
doi:10.1016/j.disc.2005.07.004 fatcat:au5qtlbudjeytpcclv2yu5c7fa

Cyclic whist tournaments

Ian Anderson, Normal J. Finizio
1994 Discrete Mathematics  
Although the existence of a Whist tournament design Wh(4n) for each n> 1 was established in the 1970s by Baker and Wilson, no new cyclic Wh(4n) was discovered since Moore's 1896 paper until Finizio constructed  ...  a number of cyclic designs with 4nS 1000.  ...  It is a remarkable fact that none of the new Whist tournaments constructed by Baker and Wilson were cyclic; the only cyclic designs known to exist by 1990 were those known by Moore almost a century before  ... 
doi:10.1016/0012-365x(94)90138-4 fatcat:unoqs65gtvc7jju2fter4wwvei

Page 2111 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
family of new bases can be produced.” 974:05049 05B30 Leonard, Philip A. (1-AZS; Tempe, AZ) Some new Z-cyclic whist tournaments.  ...  K. (4-GLAS; Glasgow) Character sums and Z-cyclic whist tournaments.  ... 

One frame and several new infinite families of Z-cyclic whist designs

Norman J Finizio
2004 Discrete Mathematics  
several new inÿnite classes of Z-cyclic whist designs.  ...  A sampling of the new results contained herein is as follows: (1) Z-cyclic Wh(3 3 p+1), p a prime of the form 4t +1; (2) Z-cyclic Wh(3 2n+1 s+1), for all n ¿ 1, s=5; 13; 17; (3) Z-cyclic Wh(3 2n s+1),  ...  Some of the results contained in this paper depend on new Z-cyclic whist designs that, as yet, do not appear in print. We cite only the designs that are utilized in this study.  ... 
doi:10.1016/s0012-365x(03)00270-x fatcat:cnavibfuivctroyfjey3dqeibq

More ZCPS-Wh(v) and several new infinite classes of Z-cyclic whist tournaments

Norman J. Finizio, Philip A. Leonard
1998 Discrete Applied Mathematics  
A Z-cyclic wh ( 148) , a new result, is presented and used to establish several new infinite classes of Z-cyclic whist tournaments. 0  ...  A Z-cyclic whist tournmant on u players having the property that the collection of initial round partner pairs form the patterned starter in Z N is known as a Z-cyclic patterned starter whist tournament  ...  Several new infinite classes of Z-cyclic W&(V) As noted earlier, the tournament of Example 1.4 extends our knowledge of ZCPS-V%(V).  ... 
doi:10.1016/s0166-218x(98)00034-1 fatcat:xik37bqinrf23kncrl6ixh5fe4

Z-cyclic whist tournaments with a patterned starter initial round

Norman J. Finizio
1994 Discrete Applied Mathematics  
If u = 1 (mod 4) we define a Z-cyclic patterned starter whist tournament on L' players, ZCPS-l+%(u), to be a cyclic whist tournament for which the set of initial round partner pairs form a patterned starter  ...  for Z,.  ...  In the special case k = 1, GF(p) = Z,, and we say that both constructions yield Z-cyclic patterned starter whist tournaments, ZCPS-Wh(v) .  ... 
doi:10.1016/0166-218x(94)90147-3 fatcat:lhhi7ixnlvh4ba745whezou4ze

Necessary conditions and frame constructions for Z-cyclic patterned starter whist tournaments

Sihuang Hu, Gennian Ge
2012 Discrete Applied Mathematics  
In this paper, we will first provide two new nonexistence results for Z-cyclic patterned starter whist tournaments.  ...  To construct Z-cyclic whist tournaments, the concept of Z-cyclic patterned starter whist tournaments was introduced. The research on Z-cyclic patterned starter whist tournaments dates back to 1954.  ...  As a by-product, we will provide two new nonexistence results for Z-cyclic patterned starter whist tournaments.  ... 
doi:10.1016/j.dam.2012.05.011 fatcat:3c3fzlgnnrahjoc7gj27i5u6ay

Page 806 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
New families of Z-cyclic directed whist and triplewhist tournaments are obtained, including some which are decompos- able into smaller whist tournaments.  ...  Thus a (v, Z;,, 1)-PCD is just a (v,k,1) perfect Mendelsohn design and so a resolved (uv, Z4, 1)-PCD is a directed whist tournament; further, a resolved (v, Z3, 1)-PCD is a triplewhist tournament.  ... 
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