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How many 7 × 7 latin squares can be partitioned into Youden squares?

D.A. Preece
1995 Discrete Mathematics  
However, the literature seems to have been silent on how many Latin squares of appropriate sizes can be partitioned in this way.  ...  We now show that, of the 564 isotopy classes (transformation sets) of 7 2:7 Latin squares, 29 consist of squares that can be partitioned into 3 x 7 and 4 x 7 Youden squares; these 29 isotopy classes belong  ...  His 7 x 7 example, with partitioning into a 3 x 7 and a 4 x 7 Youden square, is the Youden's examples invite the question 'How many Latin squares can be so partitioned?'  ... 
doi:10.1016/0012-365x(94)00216-6 fatcat:ya3exe6dubdlxj7aqotp6lra5a

Some 6 × 11 Youden squares and double Youden rectangles

D.A. Preece
1997 Discrete Mathematics  
5-cyclic Youden squares of size 6 x 11 are enumerated and classified into 70 species. In a certain standardised form, there are 249 such Youden squares. Of the 61 752 ordered pairs of  ...  The Youden squares of Table 1 can therefore be grouped into 4 pairs and so can be seen to come from four of the six species [14] of 4 x 7 Youden square.  ...  how it can be generated from just columns +, P and p.  ... 
doi:10.1016/s0012-365x(96)00254-3 fatcat:sfs5yuyzjzexbjrjjbtkqr5vhq

Page 7170 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
A. (4-KENT-MS; Canterbury) How many 7 x 7 Latin squares can be partitioned into Youden squares? (English summary) 14th British Combinatorial Conference (Keele, 1993).  ...  However, the literature seems to have been silent on how many Latin squares of appropriate sizes can be partitioned in this way.  ... 

What is a design? How should we classify them?

R. A. Bailey, Peter J. Cameron
2007 Designs, Codes and Cryptography  
In this paper we present a classification scheme which aims to include as many important types as possible, based on a balance among concept, representation and use.  ...  AMS Classification If you were to go into a motorcycle-parts department and ask them for a feedback assembly they wouldn't know what the hell you were talking about. They don't split it up that way.  ...  If the block design is balanced, this row-column design is called a Youden square [28] , but any square 1-design can be 'Youdenized' in this way.  ... 
doi:10.1007/s10623-007-9092-3 fatcat:6doe27v3onf4ppuhnqf37dx32q

Small Youden Rectangles, Near Youden Rectangles, and Their Connections to Other Row-Column Designs [article]

Gerold Jäger, Klas Markström, Denys Shcherbak, Lars-Daniel Öhman
2022 arXiv   pre-print
Finally, we also investigate certain Latin rectangles with three possible pairwise intersection sizes for the columns and demonstrate that these can give rise to triple and sesqui arrays which cannot be  ...  We have enumerated all Youden rectangles for a range of small parameter values, excluding the almost square cases where k = n-1, in a large scale computer search.  ...  Youden rectangles can be represented in different ways.  ... 
arXiv:1910.02791v3 fatcat:p4ojrmoszzbphaozvspaptodla

Enumeration and Construction of Balanced Incomplete Block Configurations

Gertrude M. Cox
1940 The Annals of Mathematical Statistics  
or quasi-Latin squares [21] can be constructed by using the completely orthogonalized squares.  ...  How- ever, these configurations can be arranged in Youden squares [22] in which all the sets are placed side by side and all the elements in a single row form a com- plete replication.  ... 
doi:10.1214/aoms/1177731943 fatcat:dyqtfunayzd4bmzzqu5u435aie


Geoffrey Beall
1971 ETS Research Bulletin Series  
Discussed are: change-over experiments; Youden fields; carry-over of treatment effects; writing Youden designs; analysis of data from latin squares, from a single Youden (txcxt) and from various special  ...  This guide presents many new experimental designs fo data analysis and reviews certain standard procedures.  ...  Since, however, there are many people, a great deal of information can be gathered fairly shortly. Accordingly, one uses a Youden rectangle.  ... 
doi:10.1002/j.2333-8504.1971.tb01018.x fatcat:gkq2xg5s2nh3vak6o6c2htwbzu

Page 5762 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
Preece, How many 7 x 7 Latin squares can be partitioned into Youden squares? (343- 352); D. A. Preece and B. J.  ...  Vowden, Graeco-Latin squares with embedded balanced superimpositions of Youden squares (353- 363); Zdenék Ryjaéek and Ingo Schiermeyer, On the independence number in K),,,\-free graphs (365-374); Abdén  ... 

Page 238 of Mathematical Reviews Vol. 57, Issue 1 [page]

1979 Mathematical Reviews  
62 5741786 238 | 239 Statistics (2n+1) objects is partitioned into s subsets 7, ---,7,, where by =(tas+1)(s™—1)s"~*/(s—1) and bg =(t,s—1)s"~ *(s"—1)/(s—1). lowet |7;| > 2 for all i; now find (n—1) other  ...  It is shown how | Simpler methods for larger b, are also discussed. of 6, these problems can be solved by the aid of Skolem sequences. J.  ... 

Designs on the web

R.A. Bailey, Peter J. Cameron, Peter Dobcsányi, John P. Morgan, Leonard H. Soicher
2006 Discrete Mathematics  
, through research topics such as "How should the concept of partial balance be extended to designs which do not have constant block size?"  ...  squares, double Youden rectangles, Freeman-Youden rectangles, SOMAs, Howell designs and Room squares.  ...  Many more examples and related results can be found in [28] .  ... 
doi:10.1016/j.disc.2004.10.027 fatcat:ry7p5ngtbvfbxga6n4tz2jsjci

Polynomial representations of complete sets of frequency hyperrectangles with prime power dimensions

Stephan J Suchower
1993 Journal of combinatorial theory. Series A  
The technique produces a wide variety of sets of mutually orthogonal frequency hyperrectangles and can be applied to the construction of orthogonal arrays of various strengths.  ...  A follow-up article will demonstrate how this new construction can be used to generate The concept of a complete set of latin squares can also be extended to F-squares, F-rectangles, and F-hyperrectangles  ...  Let {Wl ..... wl} -~Fq k be an optimal (l, d; q, k; Fq)-Set, and partition these vectors into m disjoint sets TI ..... Tm where {7],.[ = zri, 1 ~< i~< m.  ... 
doi:10.1016/0097-3165(93)90071-f fatcat:v6gbpq4b7nfb3poqyhdccqy5im

A new method of radioactive standard calibration

H.H. Seliger
1950 Journal of research of the National Bureau of Standards  
strengths are extrapolated to lower strength s, th e results of Randall and Failey [4], Hamed and Robinson [5] , and Harned and Mannweiler [6] obtained by electromotive-force methods and Weil and Morris [7]  ...  Youden and J. M .  ...  Thus even this simple application of the Chi square test is an extremely useful one for checking equipment, and in the followin g sections we shall show how it and th e method of Latin squares are used  ... 
doi:10.6028/jres.045.056 fatcat:o2tnfgvinjg5tnpqbfj2d44mwm

Teaching Design of Experiments using Hasse diagrams [article]

Hans-Michael Kaltenbach
2019 arXiv   pre-print
Specifically, we show how Hasse diagrams allow constructing most elementary designs and finding many of their properties, such as degrees of freedom, error strata, experimental units and denominators for  ...  We demonstrate how instructors can seamlessly use Hasse diagrams to construct designs by combining simple unit- and treatment structures, identify pseudo-replication, and discuss a design's randomization  ...  This model is over-parametrized, and each factor's subscript denotes how many of its parameters can be independently estimated.  ... 
arXiv:1912.08567v1 fatcat:in2glskonnhwrjpuwnjsemvr3u

Effects of Design Properties on Parameter Estimation in Large-Scale Assessments

Martin Hecht, Sebastian Weirich, Thilo Siegle, Andreas Frey
2015 Educational and Psychological Measurement  
The purpose of this study is to investigate the effects of these two design properties on bias and root mean square error of item parameter estimates from the Rasch model.  ...  The simulation results showed a small effect of position balancing on bias and root mean square error of the item parameter estimates while the cluster pair balance was ignorable.  ...  Thus, the results of the present study are providing evidence that it is unproblematic to apply these designs, which is helpful because many large and very large Youden square designs are not yet found  ... 
doi:10.1177/0013164415573311 pmid:29795851 pmcid:PMC5965600 fatcat:nglznetkjfamzcpz5grkxfutpy

NRC Designs—New Tools for Successful Agricultural Experiments

Agnieszka Łacka
2021 Agronomy  
In a nested row–column design (NRC), the experimental units in each of n blocks are grouped into n1 rows and n2 columns.  ...  It has been proposed in the literature to use many different designs to control two sources of external variation, such as Latin squares, Youden squares, generalized Youden designs, or row-column designs  ...  It can also be checked that SS(U C ) + SS(U F 1 ) + SS(U F 2 ) + SS(U F 1 F 2 ) = SS V , (15) Now one can proceed to the general ANOVA (see Appendices A.1-A.3) and its partition into four components related  ... 
doi:10.3390/agronomy11122406 fatcat:kun3nc7haveytfxoyrvb6mm6u4
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