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Generalizations of results of Stanton on BIBDs

Joseph Hammer, Dinesh G. Sarvate
<span title="">1992</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
To Ralph Stanton with much respect and appreciation. Abstract Hammer, J., D.G. Sarvate, Generalizations of results of Stanton on BIBDs, Discrete Mathematics 102 (1992) 149-154.  ...  We generalize some results of R.G. Stanton concerning intersection numbers and embeddings for balanced incomplete block designs. Majindar has proved the following (see Stanton [l]).  ...  Generalizations of results of Stanton on BIBDs 151 Proof. As proved in the above theorem y < k. But now we know the presence of only one block repeated n times.  ... 
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A Note on BIBDS

Ralph G. Stanton
<span title="">1957</span> <i title="Institute of Mathematical Statistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/do6phmpscjh2xiibivfj4saxza" style="color: black;">The Annals of Mathematical Statistics</a> </i> &nbsp;
STANTON A NOTE ON BIBDS By Raupu G.  ...  STANTON University of Toronto It is well known that the parameters (v, b, r, k, \) of a balanced incomplete block design (BIBD) satisfy the relations bk = rv, Av — 1) = r(k — 1), r—r=rk— wm.  ... 
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Page 662 of Mathematical Reviews Vol. 48, Issue 3 [page]

<span title="">1974</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A BIBD having the parameters of the residual of a BIBD is called a quasi- residual design.  ...  S. 3755 A series of counterexamples to a conjecture of Stanton and Mullin. Utilitas Math. 4 (1973), 77-85.  ... 
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Page 2869 of Mathematical Reviews Vol. , Issue 87f [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A BIBD(v, 3, A) is said to be simple if it contains no repeated triples. Using a theorem of R. G. Stanton and R. J. Collens [International colloquium on combinatorial theory, Vol.  ...  Stanton (Winnipeg, Man.) 87£:05025 Sarvate, Dinesh G. (5-SYD) All simple BIBDs with block size 3 exist. Thirteenth Australasian conference on combinatorial mathematics and computing (Sydney, 1985).  ... 
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New lower bounds for the number of blocks in balanced incomplete block designs [article]

Muhammad Ali Khan
<span title="2015-05-31">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this note we prove a new lower bound on the number of blocks b that holds for all BIBDs.  ...  We further prove that for a significantly large number of BIBDs our bound is tighter than the bounds given by the inequalities of Bose and Kageyama.  ...  Acknowledgements: The author is thankful to King Fahd University of Petroleum & Minerals for continuous research support.  ... 
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Page 2970 of Mathematical Reviews Vol. , Issue 81H [page]

<span title="">1981</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
each row [column] of the array in exactly one cell, and each k-subset of X appears in exactly one cell of the array.  ...  Stanton, Dennis Some Erdés-Ko-Rado theorems for Chevalley groups. SIAM J.  ... 
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Page 1329 of Mathematical Reviews Vol. , Issue 85d [page]

<span title="">1985</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Billington (Brisbane) Stanton, R. G. (3-MB-C) 85d:05049 The appropriateness of standard BIBD presentation. Ars Combin. 16 (1983), A, 289-296.  ...  Research on the similarity classes and on the extensions by rows of a set of t vx r permutation arrays is treated; here the results concerning Latin rectangles are remarkable.  ... 
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Page 953 of Mathematical Reviews Vol. , Issue 82c [page]

<span title="">1982</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Pavel Tomasta (Bratislava) Stanton, R. G. 82c:05021 A conjecture on quintuple systems. Ars Combin. 10 (1980), 187-192.  ...  In each case the points of the BIBD correspond to the blocks of the LBD and the blocks of the BIBD correspond to the valid pairs of the LBD.  ... 
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Page 2498 of Mathematical Reviews Vol. , Issue 81G [page]

<span title="">1981</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
To extend his result the author proves a general product theorem.  ...  The proof of the main result of part II is more difficult } than that of part I.  ... 
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Page 862 of Mathematical Reviews Vol. 43, Issue 4 [page]

<span title="">1972</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
On the basis of results of the ky +---+k,, 2(r)=1":k,!---n*sk,! and s(7)=s,"1---8,*n, | where s,=>}_, a (note the misprint in the upper sum- mation index on the line preceding formula (5)).  ...  Riordan, An intro- duction to combinatorial analysis, pp. 67-68, Wiley, New York, 1958; MR 20 #3077], one can give short proofs of these results.  ... 
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Page 3041 of Mathematical Reviews Vol. , Issue 89F [page]

<span title="">1989</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This result allows us to give simple proofs for the existence of BIBD(v, 4,2) with various additional properties.” 05B Designs and configurations 89f:05035 05B05 Robinson, Philip W. (1-ABRN) Embedding  ...  A result of R. M. Wilson [in Combinatorics, Part I (Breukelen, 1974), 18-41, Math.  ... 
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Ralph Gordon Stanton

BrendanD. McKay, Jennifer Seberry, ScottA. Vanstone
<span title="">1991</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Stanton observed that a much more enlightening classification results if one concentrates on the parameters u and k. For example, if D i?  ...  In order to cast more light on the previous areas, Stanton felt the need to study a more general class of objects called 'exact coverings (packings) with r-wise balance'.  ... 
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Page 3580 of Mathematical Reviews Vol. , Issue 92g [page]

<span title="">1992</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Mills (1-IDA) 92g:05062 05B40 Stanton, R. G. (3-MB-C); Buskens, R. W. (3-MB-C) An upper approximation to the BIBD(15, 21,7, 5, 2).  ...  The new algorithm improves on the running time of previously known algorithms by exploiting the lack of symmetry between certain circuit results and certain cocircuit results for graphs.  ... 
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Page 46 of Mathematical Reviews Vol. 58, Issue 1 [page]

<span title="">1979</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This is the first example of a nontrivial nonembeddable design on less than 16 points. Peter Eades (Queensland) 58 #279 Mullin, R. C.; Stanton, R.  ...  “The question of making it feasible for a reader to check the results, as the referee has emphasized, is the most awkward one that arises over their publication.  ... 
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Page 1233 of Mathematical Reviews Vol. , Issue 88c [page]

<span title="">1988</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
An elementary abelian S(t,k,v) is a Steiner system which has an elementary abelian collineation group of order v acting transitively on the v points. In general, the number of S(2, 4, 49) is unknown.  ...  This problem is related to the g)(v) problem of Stanton, which asks for the minimal number of blocks in a PBD of order v in which the largest block size is k.  ... 
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