The existence of howell designs of siden+1 and order 2n View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1981-09

AUTHORS

P. J. Schellenberg, D. R. Stinson, S. A. Vanstone, J. W. Yates

ABSTRACT

AHowell design of side s andorder 2n, or more briefly, anH(s, 2n), is ans×s array in which each cell either is empty or contains an unordered pair of elements from some 2n-set, sayX, such that(a) each row and each column is Latin (that is, every element ofX is in precisely one cell of each row and each column) and(b) every unordered pair of elements fromX is in at most one cell of the array. Atrivial Howell design is anH(s, 0) havingX=Ø and consisting of ans×s array of empty cells. A necessary condition onn ands for the existence of a nontrivialH(s, 2n) is that 0 More... »

PAGES

289-301

References to SciGraph publications

  • 1975-02. The existence of Room squares in AEQUATIONES MATHEMATICAE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02579335

    DOI

    http://dx.doi.org/10.1007/bf02579335

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046584364


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/08", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Information and Computing Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
              "id": "http://www.grid.ac/institutes/grid.46078.3d", 
              "name": [
                "University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Schellenberg", 
            "givenName": "P. J.", 
            "id": "sg:person.011251054473.16", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011251054473.16"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
              "id": "http://www.grid.ac/institutes/grid.46078.3d", 
              "name": [
                "University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Stinson", 
            "givenName": "D. R.", 
            "id": "sg:person.014151373147.58", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014151373147.58"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "St. Jerome\u2019s College, University of Waterloo, Canada", 
              "id": "http://www.grid.ac/institutes/grid.46078.3d", 
              "name": [
                "University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
                "St. Jerome\u2019s College, University of Waterloo, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Vanstone", 
            "givenName": "S. A.", 
            "id": "sg:person.010344544767.07", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada", 
              "id": "http://www.grid.ac/institutes/grid.46078.3d", 
              "name": [
                "University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Yates", 
            "givenName": "J. W.", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01834113", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018039054", 
              "https://doi.org/10.1007/bf01834113"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1981-09", 
        "datePublishedReg": "1981-09-01", 
        "description": "AHowell design of side s andorder 2n, or more briefly, anH(s, 2n), is ans\u00d7s array in which each cell either is empty or contains an unordered pair of elements from some 2n-set, sayX, such that(a) each row and each column is Latin (that is, every element ofX is in precisely one cell of each row and each column) and(b) every unordered pair of elements fromX is in at most one cell of the array. Atrivial Howell design is anH(s, 0) havingX=\u00d8 and consisting of ans\u00d7s array of empty cells. A necessary condition onn ands for the existence of a nontrivialH(s, 2n) is that 0
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02579335'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02579335'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02579335'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02579335'


     

    This table displays all metadata directly associated to this object as RDF triples.

    112 TRIPLES      21 PREDICATES      55 URIs      46 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf02579335 schema:about anzsrc-for:01
    2 anzsrc-for:08
    3 schema:author N242bddc609244d42b8aff2f361e8c28d
    4 schema:citation sg:pub.10.1007/bf01834113
    5 schema:datePublished 1981-09
    6 schema:datePublishedReg 1981-09-01
    7 schema:description AHowell design of side s andorder 2n, or more briefly, anH(s, 2n), is ans×s array in which each cell either is empty or contains an unordered pair of elements from some 2n-set, sayX, such that(a) each row and each column is Latin (that is, every element ofX is in precisely one cell of each row and each column) and(b) every unordered pair of elements fromX is in at most one cell of the array. Atrivial Howell design is anH(s, 0) havingX=Ø and consisting of ans×s array of empty cells. A necessary condition onn ands for the existence of a nontrivialH(s, 2n) is that 0<n≦s≦2n-1.AnH(n+t, 2n) is said to contain a maximum trivial subdesign if somet×t subarray is theH(t, 0). This paper describes a recursive construction for Howell designs containing maximum trivial subdesigns and applies it to settle the existence question forH(n+1, 2n)’s: forn+1 a positive integer, there is anH(n+1, 2n) if and only ifn+1 ∉ {2, 3, 5}.
    8 schema:genre article
    9 schema:isAccessibleForFree false
    10 schema:isPartOf N3d256720b54e4bddab7893190693ea8b
    11 Nacbf33d20d0b4b08a637786f3a97ab6b
    12 sg:journal.1136493
    13 schema:keywords Howell designs
    14 Latin
    15 ands
    16 array
    17 briefly
    18 cells
    19 column
    20 conditions
    21 consisting
    22 construction
    23 design
    24 elements
    25 empty cells
    26 existence
    27 existence question
    28 fromx
    29 integers
    30 more briefly
    31 necessary condition
    32 order
    33 pairs
    34 paper
    35 positive integer
    36 questions
    37 recursive construction
    38 rows
    39 subarrays
    40 subdesigns
    41 unordered pairs
    42 schema:name The existence of howell designs of siden+1 and order 2n
    43 schema:pagination 289-301
    44 schema:productId N838dc7e19ac242299184d688fc3a86e0
    45 Nbdf5efa852fd47a681d6723daecba1e0
    46 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046584364
    47 https://doi.org/10.1007/bf02579335
    48 schema:sdDatePublished 2022-10-01T06:27
    49 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    50 schema:sdPublisher N7a07214228cf44c29c3fc8e7c0a1c407
    51 schema:url https://doi.org/10.1007/bf02579335
    52 sgo:license sg:explorer/license/
    53 sgo:sdDataset articles
    54 rdf:type schema:ScholarlyArticle
    55 N0c96922598f04f67b47bd6ae692f03ed rdf:first sg:person.014151373147.58
    56 rdf:rest N10241ae3e1b1437cab97acd6ea4e879d
    57 N10241ae3e1b1437cab97acd6ea4e879d rdf:first sg:person.010344544767.07
    58 rdf:rest N7ab655f0493948f3bad9a1291db18b0b
    59 N242bddc609244d42b8aff2f361e8c28d rdf:first sg:person.011251054473.16
    60 rdf:rest N0c96922598f04f67b47bd6ae692f03ed
    61 N3d256720b54e4bddab7893190693ea8b schema:issueNumber 3
    62 rdf:type schema:PublicationIssue
    63 N7a07214228cf44c29c3fc8e7c0a1c407 schema:name Springer Nature - SN SciGraph project
    64 rdf:type schema:Organization
    65 N7ab655f0493948f3bad9a1291db18b0b rdf:first Nafd64c8b23594e909aceeb1723eb7265
    66 rdf:rest rdf:nil
    67 N838dc7e19ac242299184d688fc3a86e0 schema:name doi
    68 schema:value 10.1007/bf02579335
    69 rdf:type schema:PropertyValue
    70 Nacbf33d20d0b4b08a637786f3a97ab6b schema:volumeNumber 1
    71 rdf:type schema:PublicationVolume
    72 Nafd64c8b23594e909aceeb1723eb7265 schema:affiliation grid-institutes:grid.46078.3d
    73 schema:familyName Yates
    74 schema:givenName J. W.
    75 rdf:type schema:Person
    76 Nbdf5efa852fd47a681d6723daecba1e0 schema:name dimensions_id
    77 schema:value pub.1046584364
    78 rdf:type schema:PropertyValue
    79 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    80 schema:name Mathematical Sciences
    81 rdf:type schema:DefinedTerm
    82 anzsrc-for:08 schema:inDefinedTermSet anzsrc-for:
    83 schema:name Information and Computing Sciences
    84 rdf:type schema:DefinedTerm
    85 sg:journal.1136493 schema:issn 0209-9683
    86 1439-6912
    87 schema:name Combinatorica
    88 schema:publisher Springer Nature
    89 rdf:type schema:Periodical
    90 sg:person.010344544767.07 schema:affiliation grid-institutes:grid.46078.3d
    91 schema:familyName Vanstone
    92 schema:givenName S. A.
    93 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010344544767.07
    94 rdf:type schema:Person
    95 sg:person.011251054473.16 schema:affiliation grid-institutes:grid.46078.3d
    96 schema:familyName Schellenberg
    97 schema:givenName P. J.
    98 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011251054473.16
    99 rdf:type schema:Person
    100 sg:person.014151373147.58 schema:affiliation grid-institutes:grid.46078.3d
    101 schema:familyName Stinson
    102 schema:givenName D. R.
    103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014151373147.58
    104 rdf:type schema:Person
    105 sg:pub.10.1007/bf01834113 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018039054
    106 https://doi.org/10.1007/bf01834113
    107 rdf:type schema:CreativeWork
    108 grid-institutes:grid.46078.3d schema:alternateName St. Jerome’s College, University of Waterloo, Canada
    109 University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
    110 schema:name St. Jerome’s College, University of Waterloo, Canada
    111 University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada
    112 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...