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Construction of symmetric PBIB designs and related results

1981
*
Discrete Mathematics
*

In this section we shall give some

doi:10.1016/0012-365x(81)90025-x
fatcat:ro5qcccawzh2heljtvxmfozxcq
*results*on the existence an;?.*construction**of*PBYS, th.e structure introduced by Bose*and*Kishen [2:9. Consider a k x v matrix A. ... Some new*results*on existence*of*difference sets (v, k, q, hi, pjk) when the number*of*treatments is a product*of*two power primes, are presented a.nd thereby series*of**symmetric*two-associate*and*three-associate ...##
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Page 3790 of Mathematical Reviews Vol. , Issue 85i
[page]

1985
*
Mathematical Reviews
*

There is a well-known

*relation**of*triangular*and*L2 type*PBIB**designs*to the so-called line graphs in graph theory. Let G be a graph with v edges. Then its line graph L(G) has v vertices. ... Using this fact, the authors present a very simple*and*general method for*constructing*triangular*and*L2 type*PBIB**designs*, along with some practical series*of**designs*which mostly have large values*of*...##
###
Construction of PBIB designs through chosen lines and Triangles of graphs

English

2014
*
International Journal of Mathematics Trends and Technology
*

English

We have considered six configurations for this purpose

doi:10.14445/22315373/ijmtt-v8p505
fatcat:ymkaig3vqnhblenqofzyzu2ilu
*and**constructed*four two associate class*PBIB**designs**and*two three class*PBIB**designs*. ... In this paper, we have*constructed*partially balanced incomplete block (*PBIB*)*designs*with two*and*three associate classes by establishing a link between*PBIB**designs**and*graphs through the chosen lines ... graphs, as a*result*we get new*PBIB**designs*with two*and*three associate class*PBIB**designs*. ...##
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Page 652 of Mathematical Reviews Vol. , Issue 89B
[page]

1989
*
Mathematical Reviews
*

Yang [Studies on finite geometries

*and*incomplete block*designs*(Chinese), Science Press, Beijing, 1966; per bibl.], more associa- tion schemes*and**PBIB**designs*are*constructed*. ... In the paper under review, the authors substantially improve the latter*result*, using the concept*of*pairwise balanced*designs**and*other*related*combinatorial con- figurations. ...##
###
Page 471 of Mathematical Reviews Vol. , Issue 83b
[page]

1983
*
Mathematical Reviews
*

A method

*of**construction**and*some new resolvable*PBIB**designs*obtained by this method are given.” 83b:05024 Osaka J. Math. 18 (1981), no. 3, 787-799. ... .; Shrikhande, Mohan Tight subdesigns*of**symmetric*Ars Combin. 12 (1981), 303-309. Let D(v,k,A) be a*symmetric**design*containing a*symmetric**design*D,(v,,k,,A,). Let x =0,(k—k,)/(vo—0,). ...##
###
Page 2745 of Mathematical Reviews Vol. , Issue 80G
[page]

1980
*
Mathematical Reviews
*

L. 80g:62055
On

*construction**of**PBIB**designs*through 2” factorials. J. Indian Statist. Assoc. 16 (1978), 7-14. The authors generalize a method*of**construction**of**PBIB**designs*, due to G. M. ... schemes*and*embedding problems*of*Regression with given marginals. residual*designs*into the corresponding*symmetric*BIB*designs*. ...##
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BLOCKING IN PARTIAL DIALLEL CROSSES

1998
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Conference on Applied Statistics in Agriculture
*

Generally the parents are included in the experimental material for combining ability analysis for comparing the performance

doi:10.4148/2475-7772.1286
fatcat:pcu6isprcvakhb4zgjmzoww4su
*of*crosses with parents*and*also for calculating heterosis. ... Method*of*analysis*of*partial diallel crosses in incomplete blocks for the method -2*of*Griffing (1956) has been given. ... Parameters*of*this*design*are v = nO' b = v = p*and*k = r+ I The*resultant**design*happens to be a Partially Balanced n-ary*design*as defined by Tocher (I9S2). ...##
###
Page 494 of Mathematical Reviews Vol. 15, Issue 6
[page]

1954
*
Mathematical Reviews
*

It is however known that it is not always possible to integrate a

*design*with these parameters*and*to obtain a*symmetrical**design*from it through the adjunction*of*k varieties*and*one block. ... Connor, Shimamoto, Rao*and*the author, the author discusses*relations*between group-divisible*designs**and*certain special types*of*confounded two-factor*designs*. H. B. Mann (Columbus, Ohio). ...##
###
Page 4710 of Mathematical Reviews Vol. , Issue 94h
[page]

1994
*
Mathematical Reviews
*

The

*construction**of*such*designs*is closely*related*to the property P, (no ¢ columns are linearly dependent)*of*matrices with elements 0*and*1. ... The author gives a thorough survey*of*the literature, outlines proofs*of*many known*results**and*presents some new ones. He also poses some interesting problems*of**construction**of*such*designs*. ...##
###
Page 2578 of Mathematical Reviews Vol. , Issue 95e
[page]

1995
*
Mathematical Reviews
*

over finite field with characteristic 2 to

*construct**PBIB**designs*. ... By taking the set*of*hyperbolic planes containing a fixed singular line as the set*of*treatments, the authors*construct*an association scheme with g associate classes*and*some*PBIB**designs**and*compute ...##
###
Page 1964 of Mathematical Reviews Vol. , Issue 84e
[page]

1984
*
Mathematical Reviews
*

The

*construction**of*C-matrices (=information matrices in block*designs*) which are*symmetric*with respect to a group*of*permutations*of*rows*and*columns,*and**of*their*symmetric*g-inverses are discussed. ... A theorem on distribution*of*the elements*of*this set among the blocks*of*the*design*is proved*and**results**related*to certain well-known association schemes*of*three associate classes are obtained.” ...##
###
Page 6096 of Mathematical Reviews Vol. , Issue 87k
[page]

1987
*
Mathematical Reviews
*

The author also

*constructs*PBT*designs**and*PB n-ary*designs*from a*PBIB**design*based on an NC,,-scheme as well as a group divisible*PBIB**design*with a smaller number*of*blocks*and*moderate block sizes. ... A pleasant outcome*of*this theory was the*construction**of*a (71,15,3)*symmetric**design*by Beker*and*Haemers which seems to be the only example*of*a*symmetric**design*with k > \? + A*and*A>3. ...##
###
Page 1392 of Mathematical Reviews Vol. , Issue 82d
[page]

1982
*
Mathematical Reviews
*

L. 82d:05028

*Construction**of**symmetric**PBIB**designs**and**related**results*. Discrete Math. 34 (1981), no. 1, 85-87. ...*and*three-associate*PBIB**designs*are obtained. ...##
###
Page 362 of Mathematical Reviews Vol. , Issue 91A
[page]

1991
*
Mathematical Reviews
*

For triangular

*and*L; type*PBIB**designs*with two associate classes, a method*of**construction*is given which unifies earlier construc- tions*of*such*designs*but does not produce any new*results*. ... O Bhagwandas (6-INDOR) 91a:62205 62K10 Liu, Zhang Wen (PRC-ASBJ-AM); Zheng, Hong-jie (1-PAS-S)*Construction**of*triangular*and*L; type*PBIB**designs*by using BIB*designs*. ...##
###
Page 2861 of Mathematical Reviews Vol. 58, Issue 4
[page]

1979
*
Mathematical Reviews
*

As special cases

*of*their*results*, they deduce certain known inequalities*and*block structure for 2-*and*3-associate*PBIB**designs*. Damaraju Raghavarao (Philadelphia, Pa.) 58 #18940 Shah, K. ... It is then shown how several series*of**PBIB**designs*with this association scheme can be*constructed*from m-associate trian- gular*PBIB**designs*. J. A. John (Southampton) 58 # 18943 Williams, E. ...
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