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Some new Z-cyclic whist tournament designs

2005
*
Discrete Mathematics
*

Several other

doi:10.1016/j.disc.2004.08.019
fatcat:ymediekcx5hvzjnxymn3hzyjwm
*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*. ...##
###
Directed–ordered whist tournaments and (v,5,1) difference families: existence results and some new classes of Z-cyclic solutions

2004
*
Discrete Applied Mathematics
*

In addition many

doi:10.1016/j.dam.2003.12.005
fatcat:nar7p7gisjbnfpyjj2sd4xcj2q
*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 The DFs here include both*some*unpublished cases mentioned in [1] and*some**new**designs*.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. ...##
###
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

2007
*
Journal of combinatorial theory. Series A
*

As an application,

doi:10.1016/j.jcta.2006.08.011
fatcat:pf5jak7np5cx7m34qifh6cgjqm
*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. ...##
###
Classification of whist tournaments with up to 12 players

2003
*
Discrete Applied Mathematics
*

Directed

doi:10.1016/s0166-218x(02)00578-4
fatcat:k2bxwxlodrbodkwqkhphezv6de
*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] . ...##
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A new construction for Z-cyclic whist tournaments

2003
*
Discrete Applied Mathematics
*

In this paper, a

doi:10.1016/s0166-218x(03)00381-0
fatcat:gpwfq3uqufadhej4soct42qou4
*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. ...##
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Z-cyclic generalized whist frames and Z-cyclic generalized whist tournaments

2004
*
Discrete Mathematics
*

We extend their ideas to generalized

doi:10.1016/s0012-365x(03)00271-1
fatcat:ks7py2dzfngjdjbkx5njkkdfli
*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. ...##
###
On (g,4;1)-difference matrices

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) . ...

##
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Cyclic whist tournaments

1994
*
Discrete Mathematics
*

Although the existence of a

doi:10.1016/0012-365x(94)90138-4
fatcat:unoqs65gtvc7jju2fter4wwvei
*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 ...##
###
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*. ...##
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One frame and several new infinite families of Z-cyclic whist designs

2004
*
Discrete Mathematics
*

several

doi:10.1016/s0012-365x(03)00270-x
fatcat:cnavibfuivctroyfjey3dqeibq
*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. ...##
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More ZCPS-Wh(v) and several new infinite classes of Z-cyclic whist tournaments

1998
*
Discrete Applied Mathematics
*

A

doi:10.1016/s0166-218x(98)00034-1
fatcat:xik37bqinrf23kncrl6ixh5fe4
*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). ...##
###
Z-cyclic whist tournaments with a patterned starter initial round

1994
*
Discrete Applied Mathematics
*

If u = 1 (mod 4) we define a

doi:10.1016/0166-218x(94)90147-3
fatcat:lhhi7ixnlvh4ba745whezou4ze
*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) . ...##
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Necessary conditions and frame constructions for Z-cyclic patterned starter whist tournaments

2012
*
Discrete Applied Mathematics
*

In this paper, we will first provide two

doi:10.1016/j.dam.2012.05.011
fatcat:3c3fzlgnnrahjoc7gj27i5u6ay
*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*. ...##
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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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