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

1995
*
Discrete Mathematics
*

However, the literature seems to have been silent on

doi:10.1016/0012-365x(94)00216-6
fatcat:ya3exe6dubdlxj7aqotp6lra5a
*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*?' ...##
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Some 6 × 11 Youden squares and double Youden rectangles

1997
*
Discrete Mathematics
*

5-cyclic

doi:10.1016/s0012-365x(96)00254-3
fatcat:sfs5yuyzjzexbjrjjbtkqr5vhq
*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. ...##
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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. ...##
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What is a design? How should we classify them?

2007
*
Designs, Codes and Cryptography
*

In this paper we present a classification scheme which aims to include as

doi:10.1007/s10623-007-9092-3
fatcat:6doe27v3onf4ppuhnqf37dx32q
*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. ...##
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Small Youden Rectangles, Near Youden Rectangles, and Their Connections to Other Row-Column Designs
[article]

2022
*
arXiv
*
pre-print

Finally, we also investigate certain

arXiv:1910.02791v3
fatcat:p4ojrmoszzbphaozvspaptodla
*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. ...##
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Enumeration and Construction of Balanced Incomplete Block Configurations

1940
*
The Annals of Mathematical Statistics
*

or quasi-

doi:10.1214/aoms/1177731943
fatcat:dyqtfunayzd4bmzzqu5u435aie
*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. ...##
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CHANGE-OVER EXPERIMENTS IN PRACTICE

1971
*
ETS Research Bulletin Series
*

Discussed are: change-over experiments;

doi:10.1002/j.2333-8504.1971.tb01018.x
fatcat:gkq2xg5s2nh3vak6o6c2htwbzu
*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. ...##
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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 ...##
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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. ...##
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Designs on the web

2006
*
Discrete Mathematics
*

, through research topics such as "

doi:10.1016/j.disc.2004.10.027
fatcat:ry7p5ngtbvfbxga6n4tz2jsjci
*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] . ...##
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Polynomial representations of complete sets of frequency hyperrectangles with prime power dimensions

1993
*
Journal of combinatorial theory. Series A
*

The technique produces a wide variety of sets of mutually orthogonal frequency hyperrectangles and

doi:10.1016/0097-3165(93)90071-f
fatcat:v6gbpq4b7nfb3poqyhdccqy5im
*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. ...##
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A new method of radioactive standard calibration

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 [

doi:10.6028/jres.045.056
fatcat:o2tnfgvinjg5tnpqbfj2d44mwm
*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 ...##
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Teaching Design of Experiments using Hasse diagrams
[article]

2019
*
arXiv
*
pre-print

Specifically, we show

arXiv:1912.08567v1
fatcat:in2glskonnhwrjpuwnjsemvr3u
*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. ...##
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Effects of Design Properties on Parameter Estimation in Large-Scale Assessments

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

doi:10.1177/0013164415573311
pmid:29795851
pmcid:PMC5965600
fatcat:nglznetkjfamzcpz5grkxfutpy
*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 ...##
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NRC Designs—New Tools for Successful Agricultural Experiments

2021
*
Agronomy
*

In a nested row–column design (NRC), the experimental units in each of n blocks are grouped

doi:10.3390/agronomy11122406
fatcat:kun3nc7haveytfxoyrvb6mm6u4
*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 ...
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