1,721,296 research outputs found
Generalized Bhaskar Rao designs
No full textGeneralized Bhaskar Rao designs with non-zero elements from an abelian group G are constructed. In particular this paper shows that the necessary conditions are sufficient for the existence of generalized Bhaskar Rao designs with k=3 for the following groups: │G│ is odd, G=Zr2, and G=Zr2 X H where 3+│H│ and r ≥ l. It also constructs generalized Bhaskar Rao designs with v=k, which is equivalent to v rows of a generalized Hadamard matrix of order n where v ≤ n
Generalized Bhaskar Rao designs with elements from cyclic groups of even order
No full textA necessary condition is given for the existence of some Generalised Bhaskar Rao designs (GBRDs) with odd block size over cyclic groups of even order. Some constructions are given for GBRDs over cyclic groups of even order with block size 3 and with block size 4. AMS Subject Classification: 05B99 Key words and phrases: Balanced Incomplete Block Designs; Generalised Bhaskar Rao Design
On Bhaskar Rao designs of block size four
No full textWe show that Bhaskar Rao designs of type BRD(v, b, r, 4, 6) exist for v = 0,1 (mod 5) and of type BRD (v, b, r, 4,12) exist for all v ≥ 4
Generalized Bhaskar Rao designs and dihedral groups
No full textAbstractWe solve the existence problem for generalized Bhaskar Rao designs of block size 3 for an infinite family of non-abelian groups, the dihedral groups Dn, of order 2n. In our main result we show that for n⩾1 and v⩾3 the following set of conditions is necessary and sufficient for the existence of a GBRD(v,3,λ;Dn): 1.λ≡0(mod2n);2.λv(v−1)≡0(mod24)
Generalized Bhaskar Rao designs with block size three
No full textWe show that the necessary conditions λ = 0 (mod IGI), λ(v-l)=0 (mod2), λv(v 1) = [0 (mod 6) for IGI odd, (0 (mod 24) for IGI even, are sufficient for the existence of a generalized Bhaskar Rao design GBRD(v,b,r,3,λ;G) for the elementary abelian group G, of each order IGI
Bhaskar Rao designs with block size four
No full textAbstractA Bhaskar Rao design, i.e., a BRD(v,k,λ), is formed by signing the v by b incidence matrix of a BIBD(v,k,λ) so that the inner product of any two distinct rows is 0. It is proved in the literature that such designs exist for k=4 with 28 possible exceptions. In this paper, we show that a BRD is equivalent to a special kind of group divisible design (GDD). By using the knowledge of GDDs, we resolve the open cases of BRD(v,4,λ) and complete the spectrum problem on their existence
Regular group divisible designs and Bhaskar Rao designs with block size three
No full textSome recursive constructions are given for Bhaskar Rao designs. Using examples of these designs found by Shyam J. Singh, Rakesh Vyas and new ones given here we show the necessary conditions λ = 0 (mod 2), λv(v-1) = 0 (mod 24) are sufficient for the existence of Bhaskar Rao designs with one association class and block size 3. This result is used with a result of Street and Rodger to obtain regular partially balanced block designs with 2v treatments, block size 3, λ,-0, group size 2 and v groups
Existence of generalized Bhaskar Rao designs with block size 3
No full textAbstractThere are well-known necessary conditions for the existence of a generalized Bhaskar Rao design over a group G, with block size k=3. The recently proved Hall–Paige conjecture shows that these are sufficient when v=3 and λ=|G|. We prove these conditions are sufficient in general when v=3, and also when |G| is small, or when G is dicyclic. We summarize known results supporting the conjecture that these necessary conditions are always sufficient when k=3
Bose's method of differences applied to construct Bhaskar Rao designs
No full textIn this paper we show that BIBD(v,b,r,k,λ) where v = pq or pq + 1, when written in the notation of Bose's method of differences may often be used to find generalized Bhaskar Rao designs GBRD(p,b',r',k,λ;G) where G is a group of order q and vice versa. This gives many new GBRDs including a GBRD(9,5,5;Z5) and a GBRD(13,7,7;Z7)
Bose's Method of Differences Applied to Construct Bhaskar Rao Designs
No full textIn this paper we show that BIBD(v, b, r, k, λ), where v = pq or pq + 1, when written in the notation of Bose's method of differences may often be used to find generalized Bhaskar Rao designs GBRD(p, b', r', k, λ; G) where G is a group of order q and vice versa. This gives many new GBRDs including a GBRD(9, 5, 5; Z5) and a GBRD(13, 7, 7; Z7)
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