Polarities, quasi-symmetric designs, and Hamada’s conjecture View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2008-11-26

AUTHORS

Dieter Jungnickel, Vladimir D. Tonchev

ABSTRACT

We prove that every polarity of PG(2k − 1,q), where k≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to, PGk(2k,q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada’s conjecture, for any field of prime order p. Previously, only a handful of counterexamples were known. More... »

PAGES

131-140

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10623-008-9249-8

DOI

http://dx.doi.org/10.1007/s10623-008-9249-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1000248266


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": "Lehrstuhl f\u00fcr Diskrete Mathematik, Optimierung, und Operations Research, Universit\u00e4t Augsburg, 86135, Augsburg, Germany", 
          "id": "http://www.grid.ac/institutes/grid.7307.3", 
          "name": [
            "Lehrstuhl f\u00fcr Diskrete Mathematik, Optimierung, und Operations Research, Universit\u00e4t Augsburg, 86135, Augsburg, Germany"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Jungnickel", 
        "givenName": "Dieter", 
        "id": "sg:person.016273474670.91", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016273474670.91"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematical Sciences, Michigan Technological University, 49931, Houghton, MI, USA", 
          "id": "http://www.grid.ac/institutes/grid.259979.9", 
          "name": [
            "Department of Mathematical Sciences, Michigan Technological University, 49931, Houghton, MI, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Tonchev", 
        "givenName": "Vladimir D.", 
        "id": "sg:person.016227663377.94", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016227663377.94"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1023/a:1022536423514", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044386391", 
          "https://doi.org/10.1023/a:1022536423514"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01174898", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042478746", 
          "https://doi.org/10.1007/bf01174898"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1022416002358", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006996383", 
          "https://doi.org/10.1023/a:1022416002358"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02415499", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050281933", 
          "https://doi.org/10.1007/bf02415499"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1008314923487", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050774092", 
          "https://doi.org/10.1023/a:1008314923487"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10623-003-4195-y", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046159046", 
          "https://doi.org/10.1007/s10623-003-4195-y"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01388414", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014780886", 
          "https://doi.org/10.1007/bf01388414"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1016502619995", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041465213", 
          "https://doi.org/10.1023/a:1016502619995"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00146828", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047644971", 
          "https://doi.org/10.1007/bf00146828"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2008-11-26", 
    "datePublishedReg": "2008-11-26", 
    "description": "We prove that every polarity of PG(2k\u00a0\u2212\u00a01,q), where k\u2265 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to, PGk(2k,q). In particular, the case k\u00a0=\u00a02 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada\u2019s conjecture, for any field of prime order p. Previously, only a handful of counterexamples were known.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s10623-008-9249-8", 
    "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": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "51"
      }
    ], 
    "keywords": [
      "Hamada\u2019s conjecture", 
      "quasi-symmetric designs", 
      "same intersection numbers", 
      "prime order p.", 
      "intersection numbers", 
      "order p.", 
      "infinite family", 
      "conjecture", 
      "case k", 
      "counterexamples", 
      "new family", 
      "design", 
      "construction", 
      "same parameters", 
      "parameters", 
      "field", 
      "number", 
      "family", 
      "p.", 
      "handful", 
      "polarity", 
      "handful of counterexamples"
    ], 
    "name": "Polarities, quasi-symmetric designs, and Hamada\u2019s conjecture", 
    "pagination": "131-140", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1000248266"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10623-008-9249-8"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10623-008-9249-8", 
      "https://app.dimensions.ai/details/publication/pub.1000248266"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:19", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_474.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s10623-008-9249-8"
  }
]
 

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/s10623-008-9249-8'

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/s10623-008-9249-8'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10623-008-9249-8'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10623-008-9249-8'


 

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

126 TRIPLES      22 PREDICATES      56 URIs      39 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10623-008-9249-8 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Ne240f6aec7d14afaac429e10725e1376
4 schema:citation sg:pub.10.1007/bf00146828
5 sg:pub.10.1007/bf01174898
6 sg:pub.10.1007/bf01388414
7 sg:pub.10.1007/bf02415499
8 sg:pub.10.1007/s10623-003-4195-y
9 sg:pub.10.1023/a:1008314923487
10 sg:pub.10.1023/a:1016502619995
11 sg:pub.10.1023/a:1022416002358
12 sg:pub.10.1023/a:1022536423514
13 schema:datePublished 2008-11-26
14 schema:datePublishedReg 2008-11-26
15 schema:description We prove that every polarity of PG(2k − 1,q), where k≥ 2, gives rise to a design with the same parameters and the same intersection numbers as, but not isomorphic to, PGk(2k,q). In particular, the case k = 2 yields a new family of quasi-symmetric designs. We also show that our construction provides an infinite family of counterexamples to Hamada’s conjecture, for any field of prime order p. Previously, only a handful of counterexamples were known.
16 schema:genre article
17 schema:inLanguage en
18 schema:isAccessibleForFree false
19 schema:isPartOf N78e17697955e4364a8b3eec02b0d86f1
20 Ne14b6fdcb6ec4324bf4bfa3f71e36c63
21 sg:journal.1136552
22 schema:keywords Hamada’s conjecture
23 case k
24 conjecture
25 construction
26 counterexamples
27 design
28 family
29 field
30 handful
31 handful of counterexamples
32 infinite family
33 intersection numbers
34 new family
35 number
36 order p.
37 p.
38 parameters
39 polarity
40 prime order p.
41 quasi-symmetric designs
42 same intersection numbers
43 same parameters
44 schema:name Polarities, quasi-symmetric designs, and Hamada’s conjecture
45 schema:pagination 131-140
46 schema:productId Nb33b52fdc7d1466fa704c35eabc2a334
47 Nf79e61b075434f44bf54dfd81886984e
48 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000248266
49 https://doi.org/10.1007/s10623-008-9249-8
50 schema:sdDatePublished 2022-01-01T18:19
51 schema:sdLicense https://scigraph.springernature.com/explorer/license/
52 schema:sdPublisher N56947cb413ac4c82bb3f48e2cf9ce65a
53 schema:url https://doi.org/10.1007/s10623-008-9249-8
54 sgo:license sg:explorer/license/
55 sgo:sdDataset articles
56 rdf:type schema:ScholarlyArticle
57 N56947cb413ac4c82bb3f48e2cf9ce65a schema:name Springer Nature - SN SciGraph project
58 rdf:type schema:Organization
59 N78e17697955e4364a8b3eec02b0d86f1 schema:volumeNumber 51
60 rdf:type schema:PublicationVolume
61 Nb33b52fdc7d1466fa704c35eabc2a334 schema:name doi
62 schema:value 10.1007/s10623-008-9249-8
63 rdf:type schema:PropertyValue
64 Ndf27c46d7e634d7e913c319de32d7209 rdf:first sg:person.016227663377.94
65 rdf:rest rdf:nil
66 Ne14b6fdcb6ec4324bf4bfa3f71e36c63 schema:issueNumber 2
67 rdf:type schema:PublicationIssue
68 Ne240f6aec7d14afaac429e10725e1376 rdf:first sg:person.016273474670.91
69 rdf:rest Ndf27c46d7e634d7e913c319de32d7209
70 Nf79e61b075434f44bf54dfd81886984e schema:name dimensions_id
71 schema:value pub.1000248266
72 rdf:type schema:PropertyValue
73 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
74 schema:name Mathematical Sciences
75 rdf:type schema:DefinedTerm
76 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
77 schema:name Pure Mathematics
78 rdf:type schema:DefinedTerm
79 sg:journal.1136552 schema:issn 0925-1022
80 1573-7586
81 schema:name Designs, Codes and Cryptography
82 schema:publisher Springer Nature
83 rdf:type schema:Periodical
84 sg:person.016227663377.94 schema:affiliation grid-institutes:grid.259979.9
85 schema:familyName Tonchev
86 schema:givenName Vladimir D.
87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016227663377.94
88 rdf:type schema:Person
89 sg:person.016273474670.91 schema:affiliation grid-institutes:grid.7307.3
90 schema:familyName Jungnickel
91 schema:givenName Dieter
92 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016273474670.91
93 rdf:type schema:Person
94 sg:pub.10.1007/bf00146828 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047644971
95 https://doi.org/10.1007/bf00146828
96 rdf:type schema:CreativeWork
97 sg:pub.10.1007/bf01174898 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042478746
98 https://doi.org/10.1007/bf01174898
99 rdf:type schema:CreativeWork
100 sg:pub.10.1007/bf01388414 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014780886
101 https://doi.org/10.1007/bf01388414
102 rdf:type schema:CreativeWork
103 sg:pub.10.1007/bf02415499 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050281933
104 https://doi.org/10.1007/bf02415499
105 rdf:type schema:CreativeWork
106 sg:pub.10.1007/s10623-003-4195-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1046159046
107 https://doi.org/10.1007/s10623-003-4195-y
108 rdf:type schema:CreativeWork
109 sg:pub.10.1023/a:1008314923487 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050774092
110 https://doi.org/10.1023/a:1008314923487
111 rdf:type schema:CreativeWork
112 sg:pub.10.1023/a:1016502619995 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041465213
113 https://doi.org/10.1023/a:1016502619995
114 rdf:type schema:CreativeWork
115 sg:pub.10.1023/a:1022416002358 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006996383
116 https://doi.org/10.1023/a:1022416002358
117 rdf:type schema:CreativeWork
118 sg:pub.10.1023/a:1022536423514 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044386391
119 https://doi.org/10.1023/a:1022536423514
120 rdf:type schema:CreativeWork
121 grid-institutes:grid.259979.9 schema:alternateName Department of Mathematical Sciences, Michigan Technological University, 49931, Houghton, MI, USA
122 schema:name Department of Mathematical Sciences, Michigan Technological University, 49931, Houghton, MI, USA
123 rdf:type schema:Organization
124 grid-institutes:grid.7307.3 schema:alternateName Lehrstuhl für Diskrete Mathematik, Optimierung, und Operations Research, Universität Augsburg, 86135, Augsburg, Germany
125 schema:name Lehrstuhl für Diskrete Mathematik, Optimierung, und Operations Research, Universität Augsburg, 86135, Augsburg, Germany
126 rdf:type schema:Organization
 




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


...