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Constructions and uses of incomplete pairwise balanced designs
We give explicit constructions for incomplete pairwise balanced designs IPBD(( v ; w ), K ), or, equivalently, edge-decompositions of a difference of two cliques K v \ K w into cliques whose sizes belong to the set K . Our constructions produce such designs whenever v and w satisfy the usual divis...
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| Published in: | Designs, codes, and cryptography codes, and cryptography, 2019-12, Vol.87 (12), p.2729-2751 |
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| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c319t-f0ce3f73d04a3591640d6b07658975b65088bdda89014f5c97fdff5c957120863 |
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| cites | cdi_FETCH-LOGICAL-c319t-f0ce3f73d04a3591640d6b07658975b65088bdda89014f5c97fdff5c957120863 |
| container_end_page | 2751 |
| container_issue | 12 |
| container_start_page | 2729 |
| container_title | Designs, codes, and cryptography |
| container_volume | 87 |
| creator | Dukes, Peter J. Lamken, Esther R. |
| description | We give explicit constructions for incomplete pairwise balanced designs IPBD((
v
;
w
),
K
), or, equivalently, edge-decompositions of a difference of two cliques
K
v
\
K
w
into cliques whose sizes belong to the set
K
. Our constructions produce such designs whenever
v
and
w
satisfy the usual divisibility conditions, have ratio
v
/
w
bounded away from the smallest value in
K
minus one, say
v
/
w
>
k
-
1
+
ϵ
, for
k
=
min
K
and
ϵ
>
0
, and are sufficiently large (depending on
K
and
ϵ
). As a consequence, some new results are obtained on many related designs, including class-uniformly resolvable designs, incomplete mutually orthogonal latin squares, and group divisible designs. We also include several other applications that illustrate the power of using IPBDs as ‘templates’. |
| doi_str_mv | 10.1007/s10623-019-00645-6 |
| format | article |
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v
;
w
),
K
), or, equivalently, edge-decompositions of a difference of two cliques
K
v
\
K
w
into cliques whose sizes belong to the set
K
. Our constructions produce such designs whenever
v
and
w
satisfy the usual divisibility conditions, have ratio
v
/
w
bounded away from the smallest value in
K
minus one, say
v
/
w
>
k
-
1
+
ϵ
, for
k
=
min
K
and
ϵ
>
0
, and are sufficiently large (depending on
K
and
ϵ
). As a consequence, some new results are obtained on many related designs, including class-uniformly resolvable designs, incomplete mutually orthogonal latin squares, and group divisible designs. We also include several other applications that illustrate the power of using IPBDs as ‘templates’.</description><identifier>ISSN: 0925-1022</identifier><identifier>EISSN: 1573-7586</identifier><identifier>DOI: 10.1007/s10623-019-00645-6</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Arrays ; Circuits ; Coding and Information Theory ; Computer Science ; Cryptology ; Data Structures and Information Theory ; Discrete Mathematics in Computer Science ; Information and Communication ; Latin square design</subject><ispartof>Designs, codes, and cryptography, 2019-12, Vol.87 (12), p.2729-2751</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-f0ce3f73d04a3591640d6b07658975b65088bdda89014f5c97fdff5c957120863</citedby><cites>FETCH-LOGICAL-c319t-f0ce3f73d04a3591640d6b07658975b65088bdda89014f5c97fdff5c957120863</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Dukes, Peter J.</creatorcontrib><creatorcontrib>Lamken, Esther R.</creatorcontrib><title>Constructions and uses of incomplete pairwise balanced designs</title><title>Designs, codes, and cryptography</title><addtitle>Des. Codes Cryptogr</addtitle><description>We give explicit constructions for incomplete pairwise balanced designs IPBD((
v
;
w
),
K
), or, equivalently, edge-decompositions of a difference of two cliques
K
v
\
K
w
into cliques whose sizes belong to the set
K
. Our constructions produce such designs whenever
v
and
w
satisfy the usual divisibility conditions, have ratio
v
/
w
bounded away from the smallest value in
K
minus one, say
v
/
w
>
k
-
1
+
ϵ
, for
k
=
min
K
and
ϵ
>
0
, and are sufficiently large (depending on
K
and
ϵ
). As a consequence, some new results are obtained on many related designs, including class-uniformly resolvable designs, incomplete mutually orthogonal latin squares, and group divisible designs. We also include several other applications that illustrate the power of using IPBDs as ‘templates’.</description><subject>Arrays</subject><subject>Circuits</subject><subject>Coding and Information Theory</subject><subject>Computer Science</subject><subject>Cryptology</subject><subject>Data Structures and Information Theory</subject><subject>Discrete Mathematics in Computer Science</subject><subject>Information and Communication</subject><subject>Latin square design</subject><issn>0925-1022</issn><issn>1573-7586</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKxDAURYMoOI7-gKuA6-h7SZO0G0EGHYUBN7oOaZMMHWbSmrSIf2_HCu5c3bc49z44hFwj3CKAvssIigsGWDEAVUimTsgCpRZMy1KdkgVUXDIEzs_JRc47AEABfEHuV13MQxqboZ0OaqOjY_aZdoG2sekO_d4Pnva2TZ9t9rS2exsb76jzud3GfEnOgt1nf_WbS_L-9Pi2emab1_XL6mHDGoHVwAI0XgQtHBRWyApVAU7VoJUsKy1rJaEsa-dsWQEWQTaVDi4cU2rkUCqxJDfzbp-6j9Hnwey6McXppeECUegCCzlRfKaa1OWcfDB9ag82fRkEc_RkZk9m8mR-PJnjtJhLeYLj1qe_6X9a38nqaew</recordid><startdate>20191201</startdate><enddate>20191201</enddate><creator>Dukes, Peter J.</creator><creator>Lamken, Esther R.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20191201</creationdate><title>Constructions and uses of incomplete pairwise balanced designs</title><author>Dukes, Peter J. ; Lamken, Esther R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-f0ce3f73d04a3591640d6b07658975b65088bdda89014f5c97fdff5c957120863</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Arrays</topic><topic>Circuits</topic><topic>Coding and Information Theory</topic><topic>Computer Science</topic><topic>Cryptology</topic><topic>Data Structures and Information Theory</topic><topic>Discrete Mathematics in Computer Science</topic><topic>Information and Communication</topic><topic>Latin square design</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Dukes, Peter J.</creatorcontrib><creatorcontrib>Lamken, Esther R.</creatorcontrib><collection>CrossRef</collection><jtitle>Designs, codes, and cryptography</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Dukes, Peter J.</au><au>Lamken, Esther R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Constructions and uses of incomplete pairwise balanced designs</atitle><jtitle>Designs, codes, and cryptography</jtitle><stitle>Des. Codes Cryptogr</stitle><date>2019-12-01</date><risdate>2019</risdate><volume>87</volume><issue>12</issue><spage>2729</spage><epage>2751</epage><pages>2729-2751</pages><issn>0925-1022</issn><eissn>1573-7586</eissn><abstract>We give explicit constructions for incomplete pairwise balanced designs IPBD((
v
;
w
),
K
), or, equivalently, edge-decompositions of a difference of two cliques
K
v
\
K
w
into cliques whose sizes belong to the set
K
. Our constructions produce such designs whenever
v
and
w
satisfy the usual divisibility conditions, have ratio
v
/
w
bounded away from the smallest value in
K
minus one, say
v
/
w
>
k
-
1
+
ϵ
, for
k
=
min
K
and
ϵ
>
0
, and are sufficiently large (depending on
K
and
ϵ
). As a consequence, some new results are obtained on many related designs, including class-uniformly resolvable designs, incomplete mutually orthogonal latin squares, and group divisible designs. We also include several other applications that illustrate the power of using IPBDs as ‘templates’.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10623-019-00645-6</doi><tpages>23</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0925-1022 |
| ispartof | Designs, codes, and cryptography, 2019-12, Vol.87 (12), p.2729-2751 |
| issn | 0925-1022 1573-7586 |
| language | eng |
| recordid | cdi_proquest_journals_2311374145 |
| source | Springer Nature |
| subjects | Arrays Circuits Coding and Information Theory Computer Science Cryptology Data Structures and Information Theory Discrete Mathematics in Computer Science Information and Communication Latin square design |
| title | Constructions and uses of incomplete pairwise balanced designs |
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