Complete Systems of Lines on a Hermitian Surface over a Finite Field View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1999-09

AUTHORS

G. L. Ebert, J. W. P. Hirschfeld

ABSTRACT

The aim is to find the maximum size of a set of mutually ske lines on a nonsingular Hermitian surface in PG(3, q) for various values of q. For q = 9 such extremal sets are intricate combinatorial structures intimately connected ith hemisystems, subreguli, and commuting null polarities. It turns out they are also closely related to the classical quartic surface of Kummer. Some bounds and examples are also given in the general case. More... »

PAGES

253-268

References to SciGraph publications

  • 1996-05. m-Systems and partialm-systems of polar spaces in DESIGNS, CODES AND CRYPTOGRAPHY
  • 1965-12. Forme e geometrie hermitiane, con particolare riguardo al caso finito in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1026439528939

    DOI

    http://dx.doi.org/10.1023/a:1026439528939

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1033866841


    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/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Mathematical Sciences, University of Delaare, 19716, Neark, Delaware, U.S.A", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "Department of Mathematical Sciences, University of Delaare, 19716, Neark, Delaware, U.S.A"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ebert", 
            "givenName": "G. L.", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH, East Sussex, U.K", 
              "id": "http://www.grid.ac/institutes/grid.12082.39", 
              "name": [
                "School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH, East Sussex, U.K"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hirschfeld", 
            "givenName": "J. W. P.", 
            "id": "sg:person.012124570705.64", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012124570705.64"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf00130581", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004681324", 
              "https://doi.org/10.1007/bf00130581"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02410088", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024477870", 
              "https://doi.org/10.1007/bf02410088"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1999-09", 
        "datePublishedReg": "1999-09-01", 
        "description": "The aim is to find the maximum size of a set of mutually ske lines on a nonsingular Hermitian surface in PG(3, q) for various values of q. For q = 9 such extremal sets are intricate combinatorial structures intimately connected ith hemisystems, subreguli, and commuting null polarities. It turns out they are also closely related to the classical quartic surface of Kummer. Some bounds and examples are also given in the general case.", 
        "genre": "article", 
        "id": "sg:pub.10.1023/a:1026439528939", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136552", 
            "issn": [
              "0925-1022", 
              "1573-7586"
            ], 
            "name": "Designs, Codes and Cryptography", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1-3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "17"
          }
        ], 
        "keywords": [
          "Hermitian surface", 
          "combinatorial structure", 
          "finite field", 
          "general case", 
          "extremal sets", 
          "quartic surfaces", 
          "complete system", 
          "bounds", 
          "hemisystems", 
          "Kummer", 
          "maximum size", 
          "set", 
          "surface", 
          "field", 
          "system", 
          "structure", 
          "lines", 
          "cases", 
          "values", 
          "size", 
          "example", 
          "polarity", 
          "aim"
        ], 
        "name": "Complete Systems of Lines on a Hermitian Surface over a Finite Field", 
        "pagination": "253-268", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1033866841"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1023/a:1026439528939"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1023/a:1026439528939", 
          "https://app.dimensions.ai/details/publication/pub.1033866841"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-05-10T09:52", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_338.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1023/a:1026439528939"
      }
    ]
     

    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.10.1023/a:1026439528939'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1026439528939'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1026439528939'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1026439528939'


     

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

    98 TRIPLES      22 PREDICATES      51 URIs      41 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1023/a:1026439528939 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N710a050409e841be9a36f03b61d2ef50
    4 schema:citation sg:pub.10.1007/bf00130581
    5 sg:pub.10.1007/bf02410088
    6 schema:datePublished 1999-09
    7 schema:datePublishedReg 1999-09-01
    8 schema:description The aim is to find the maximum size of a set of mutually ske lines on a nonsingular Hermitian surface in PG(3, q) for various values of q. For q = 9 such extremal sets are intricate combinatorial structures intimately connected ith hemisystems, subreguli, and commuting null polarities. It turns out they are also closely related to the classical quartic surface of Kummer. Some bounds and examples are also given in the general case.
    9 schema:genre article
    10 schema:inLanguage en
    11 schema:isAccessibleForFree false
    12 schema:isPartOf N1f23ba1922084f35a7754203afa44c43
    13 N8106fd427ff8412a9f5055576d7ba343
    14 sg:journal.1136552
    15 schema:keywords Hermitian surface
    16 Kummer
    17 aim
    18 bounds
    19 cases
    20 combinatorial structure
    21 complete system
    22 example
    23 extremal sets
    24 field
    25 finite field
    26 general case
    27 hemisystems
    28 lines
    29 maximum size
    30 polarity
    31 quartic surfaces
    32 set
    33 size
    34 structure
    35 surface
    36 system
    37 values
    38 schema:name Complete Systems of Lines on a Hermitian Surface over a Finite Field
    39 schema:pagination 253-268
    40 schema:productId N30ea014a123941d4b1264d88030c04c9
    41 Nba33f3c359c14b8bb4265ac7e201a942
    42 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033866841
    43 https://doi.org/10.1023/a:1026439528939
    44 schema:sdDatePublished 2022-05-10T09:52
    45 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    46 schema:sdPublisher N213532e797274eb68f330d95172ebed2
    47 schema:url https://doi.org/10.1023/a:1026439528939
    48 sgo:license sg:explorer/license/
    49 sgo:sdDataset articles
    50 rdf:type schema:ScholarlyArticle
    51 N1f23ba1922084f35a7754203afa44c43 schema:volumeNumber 17
    52 rdf:type schema:PublicationVolume
    53 N213532e797274eb68f330d95172ebed2 schema:name Springer Nature - SN SciGraph project
    54 rdf:type schema:Organization
    55 N30ea014a123941d4b1264d88030c04c9 schema:name doi
    56 schema:value 10.1023/a:1026439528939
    57 rdf:type schema:PropertyValue
    58 N454e8760ac344913aabfa678a583bf1c schema:affiliation grid-institutes:None
    59 schema:familyName Ebert
    60 schema:givenName G. L.
    61 rdf:type schema:Person
    62 N710a050409e841be9a36f03b61d2ef50 rdf:first N454e8760ac344913aabfa678a583bf1c
    63 rdf:rest Ndd4f71f8b5114e8897af09bec3fb0b55
    64 N8106fd427ff8412a9f5055576d7ba343 schema:issueNumber 1-3
    65 rdf:type schema:PublicationIssue
    66 Nba33f3c359c14b8bb4265ac7e201a942 schema:name dimensions_id
    67 schema:value pub.1033866841
    68 rdf:type schema:PropertyValue
    69 Ndd4f71f8b5114e8897af09bec3fb0b55 rdf:first sg:person.012124570705.64
    70 rdf:rest rdf:nil
    71 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    72 schema:name Mathematical Sciences
    73 rdf:type schema:DefinedTerm
    74 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Pure Mathematics
    76 rdf:type schema:DefinedTerm
    77 sg:journal.1136552 schema:issn 0925-1022
    78 1573-7586
    79 schema:name Designs, Codes and Cryptography
    80 schema:publisher Springer Nature
    81 rdf:type schema:Periodical
    82 sg:person.012124570705.64 schema:affiliation grid-institutes:grid.12082.39
    83 schema:familyName Hirschfeld
    84 schema:givenName J. W. P.
    85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012124570705.64
    86 rdf:type schema:Person
    87 sg:pub.10.1007/bf00130581 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004681324
    88 https://doi.org/10.1007/bf00130581
    89 rdf:type schema:CreativeWork
    90 sg:pub.10.1007/bf02410088 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024477870
    91 https://doi.org/10.1007/bf02410088
    92 rdf:type schema:CreativeWork
    93 grid-institutes:None schema:alternateName Department of Mathematical Sciences, University of Delaare, 19716, Neark, Delaware, U.S.A
    94 schema:name Department of Mathematical Sciences, University of Delaare, 19716, Neark, Delaware, U.S.A
    95 rdf:type schema:Organization
    96 grid-institutes:grid.12082.39 schema:alternateName School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH, East Sussex, U.K
    97 schema:name School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH, East Sussex, U.K
    98 rdf:type schema:Organization
     




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


    ...