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On the construction of handcuffed designs

J.F Lawless
<span title="">1974</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z77xaqun7bcxjkh75wb7iseaty" style="color: black;">Journal of combinatorial theory. Series A</a> </i> &nbsp;
In this paper we show how difference methods can be applied to the construction of handcuffed designs. The methods are powerful, and a number of families of designs are constructed.  ...  Hence, the design formed is, in fact, the desired type of handcuffed design. An example should make the construction clear. E XAMPLE.  ...  to the construction of handcuffed (u, k, h) designs.  ... 
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Handcuffed designs

Stephen H.Y. Hung, N.S. Mendelsohn
<span title="">1977</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
Handcuffed designs arc a parttcular case of block designs or, gruphs.  ...  The collection of handcuffed blocks constitutes a handcuffed design if the fnllowing are satisfied: (1) each element of the u-set appars amongst the blocks the same number of times (and at most once in  ...  hWoduction Handcuffed designs are a particular case of block designs on graphs, A handcuffed design with parameters ty, k, A consists of a system of or&red k -subsctts of a tr-set, called handcuffed blocks  ... 
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Page 27 of Mathematical Reviews Vol. 51, Issue 1 [page]

<span title="">1976</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 number of recent approaches to the construction of BIBD’s are then discussed, including the use of permutation groups, and a number of attacks on some of the more “interesting” unknown designs, such  ...  A collection of 5 handcuffed blocks forms a handcuffed design if (i) each element of the v-set appears in exactly r blocks, (ii) each (unordered) pair of distinct elements of the v-set is handcuffed in  ... 
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Balanced generalized handcuffed designs

Francis Maurin
<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;
The definition of balanced generalized handcuffed designs (BHD) is of course more specific than that of the generalized handcuffed designs that we introduced in 1987.  ...  We also show how this difference method can be made more useful in the case where the set V on which a BHD is constructed is the residue classes of integers mod V.  ...  Using a 'difference method' for the constructing of balanced generalized designs In [3] , we used a difference method in order to construct generalized handcuffed designs and this method came out as a  ... 
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Page 2448 of Mathematical Reviews Vol. , Issue 94e [page]

<span title="">1994</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;
Summary: “The definition of balanced generalized handcuffed de- signs (BHDs) is of course more specific than that of the generalized handcuffed designs that we introduced in 1987.  ...  Summary: “In this paper we give a complete solution of the ex- istence problem of handcuffed designs H(v,3,1) having an oval.  ... 
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Page 1439 of Mathematical Reviews Vol. 48, Issue 5 [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;
On the construction of handcuffed designs. J. Combinatorial Theory Ser. A 16 (1974), 76-86.  ...  The case when A=1 or 2 was also proved by S. H. Y. Hung and N. S. Mendelsohn (““Handcuffed designs’’, same J., to appear) who originally introduced the concept of handcuffed designs. K.  ... 
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Page 727 of Mathematical Reviews Vol. 56, Issue 3 [page]

<span title="">1978</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;
S. 5318 Handcuffed designs. Discrete Math. 18 (1977), no. 1, 23-33. A handcuffed design with parameters (v, k, A) consists of a set of ordered k-subsets of a v-set, the k-subsets being called blocks.  ...  A handcuffed design consists of a set of b blocks such that (1) each element of the v-set appears in exactly b blocks, (2) each pair of distinct elements is handcuffed in exactly blocks.  ... 
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On the existence of (v, 4, 3, 1)-BHDs

Francis Maurin
<span title="">1995</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/civgv5utqzhu7aj6voo6vc5vx4" style="color: black;">Discrete Mathematics</a> </i> &nbsp;
We prove that it is necessary and sufficient for a (v, 4, 3, 1)-BHD (balanced generalized handcuffed design) to exist that either v = 6n + 2 (n integer >~ 1) or v = 6n + 4 (n integer >~ 0).  ...  The set of the following 2 blocks {(0, 1, 2, 3), (1, 3, 0, 2)} is a (4, 4, 3, 1)-BHD constructed on {0, 1, 2, 3}. Remark 3.  ...  If fl is also a (v, k, 0, 20)-HD, V0 ~< t, we may say that fl is a balanced generalized handcuffed design and we name it a (v, k, t, 2)-BHD. t will be called the strength of the (v, k, t, 2)-BHD.  ... 
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Page 4145 of Mathematical Reviews Vol. , Issue 92h [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;
A 16 (1974), 76-86; MR 48 #8262] constructed a class of handcuffed designs using difference sets under the assumption that v is a prime power number.  ...  (English summary) [A method for constructing handcuffed designs] Publ. Math. Debrecen 38 (1991), no. 1-2, 13-17.  ... 
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Generalized handcuffed designs

Francis Maurin
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z77xaqun7bcxjkh75wb7iseaty" style="color: black;">Journal of combinatorial theory. Series A</a> </i> &nbsp;
As a conclusion, we use parts 1 and 2 in order to point out the existence of three particular classes of generalized handcuffed designs.  ...  The definition of generalized handcuffed designs given in this article includes, as a particular case, the definition given by Hung, Mendelsohn, and J. F. Lawless.  ...  In the blocks of p, let us replace a, by y. We then obtain a(v, k, t, A)-HD PI constructed on V' -(a,>, I,= (B,; i= l,..., b}.  ... 
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Page 4622 of Mathematical Reviews Vol. , Issue 2000g [page]

<span title="">2000</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 paper considers the construction of such systems. A fundamental construction is given for a GS(2, 3, n, 2) and other constructions determined which depend on this fun- damental one.  ...  For each n = 1 (mod 8) and for each s € {2,3} we determine all the integers v such that there is a 4-cycle system of order n containing a handcuffed design of order v and block size s.”  ... 
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Page 5591 of Mathematical Reviews Vol. , Issue 90J [page]

<span title="">1990</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;
as one, then @ is called an incomplete handcuffed design, denoted by (v,v,,k,A,r,r)-IHD.  ...  The author gives a construction of balanced ternary designs and uses it to obtain the so-called partially balanced ternary designs. Sharad S.  ... 
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Page 38 of Criminal Law & Justice Weekly Vol. 157, Issue 3 [page]

<span title="1993-01-16">1993</span> <i title="ELSEVIER LTD."> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_criminal-law-justice-weekly" style="color: black;">Criminal Law &amp; Justice Weekly </a> </i> &nbsp;
Security will naturally vary from one building to another, and from area to area, depending upon the age, the quality of design and construction, and the — forms of criminality with which particular enches  ...  In Vratsides, on the other hand, the Court of Appeal spoke approvingly of any possible prejudice to a handcuffed defendant being satisfactorily offset by a suitably worded warning.  ... 
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Page 33 of Mathematical Reviews Vol. , Issue 96a [page]

<span title="">1996</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;
Summary: “Two kinds of concepts on dualization of designs are applied to construct nested balanced incomplete block designs and 2-associate partially balanced incomplete block designs, by use of symmetric  ...  Many (often well-known) constructions appear in the proof; variations give the necessary knowledge of the chromatic numbers of the resulting designs.  ... 
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Page 659 of Mathematical Reviews Vol. , Issue 88b [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;
New families of 4- designs are also constructed. Sanpei Kageyama (Hiroshima) 88b:05026 05B05 Manrin, Francis Construction de plans en bloc de chainettes. [Construction of handcuffed designs] Publ.  ...  This is a very interesting paper on the “point-extension” method of construction of t-designs with even or odd numbers of points from another f-design for general t under some parametric restriction.  ... 
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