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Construction of symmetric PBIB designs and related results

B.L. Misra, M.L. Chandak
1981 Discrete Mathematics  
In this section we shall give some 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  ... 
doi:10.1016/0012-365x(81)90025-x fatcat:ro5qcccawzh2heljtvxmfozxcq

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

Davinder Kumar Garg
2014 International Journal of Mathematics Trends and Technology  
We have considered six configurations for this purpose 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.  ... 
doi:10.14445/22315373/ijmtt-v8p505 fatcat:ymkaig3vqnhblenqofzyzu2ilu

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.  ... 


D. R. Aneja, L . S. Kaushik
1998 Conference on Applied Statistics in Agriculture  
Generally the parents are included in the experimental material for combining ability analysis for comparing the performance 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).  ... 
doi:10.4148/2475-7772.1286 fatcat:pcu6isprcvakhb4zgjmzoww4su

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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