Regularity of certain diophantine equations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

Bidisha Roy, Subha Sarkar

ABSTRACT

In Ramsey theory, there is a vast literature on regularity questions of linear diophantine equations. Some problems in higher degree have been considered recently. Here, we show that, for every pair of positive integers r and n, there exists an integer B=B(r) such that the diophantine equation ∏m=1n∑i=1kmam,ixm,i-∑j=1lmbm,jym,j=Bwith ∑i=1kmam,i=∑j=1lmbm,j∀m=1,…,nis r-regular, where km, lm are also positive integers and am,i,bm,j are non-zero integers. More... »

PAGES

19

References to SciGraph publications

  • 2017. On a Conjecture of Fox and Kleitman on the Degree of Regularity of a Certain Linear Equation in COMBINATORIAL AND ADDITIVE NUMBER THEORY II
  • 1933-12. Studien zur Kombinatorik in MATHEMATISCHE ZEITSCHRIFT
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s12044-019-0463-2

    DOI

    http://dx.doi.org/10.1007/s12044-019-0463-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112141885


    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/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "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"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Harish-Chandra Research Institute", 
              "id": "https://www.grid.ac/institutes/grid.450311.2", 
              "name": [
                "Harish-Chandra Research Institute, HBNI, Chhatnag Road, 211 019, Jhunsi, Allahabad, India"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Roy", 
            "givenName": "Bidisha", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Harish-Chandra Research Institute", 
              "id": "https://www.grid.ac/institutes/grid.450311.2", 
              "name": [
                "Harish-Chandra Research Institute, HBNI, Chhatnag Road, 211 019, Jhunsi, Allahabad, India"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sarkar", 
            "givenName": "Subha", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1016/j.jcta.2005.07.004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015583004"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jcta.2005.07.004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015583004"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01188632", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016969098", 
              "https://doi.org/10.1007/bf01188632"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jcta.2009.02.009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1018714657"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/9783110925098.1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1086769133"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4064/aa-27-1-199-245", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1091814301"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.disc.2017.08.040", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1091942932"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.ejc.2017.11.008", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099717560"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-319-68032-3_1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1100395159", 
              "https://doi.org/10.1007/978-3-319-68032-3_1"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-04", 
        "datePublishedReg": "2019-04-01", 
        "description": "In Ramsey theory, there is a vast literature on regularity questions of linear diophantine equations. Some problems in higher degree have been considered recently. Here, we show that, for every pair of positive integers r and n, there exists an integer B=B(r) such that the diophantine equation \u220fm=1n\u2211i=1kmam,ixm,i-\u2211j=1lmbm,jym,j=Bwith \u2211i=1kmam,i=\u2211j=1lmbm,j\u2200m=1,\u2026,nis r-regular, where km, lm are also positive integers and am,i,bm,j are non-zero integers.", 
        "genre": "non_research_article", 
        "id": "sg:pub.10.1007/s12044-019-0463-2", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1320093", 
            "issn": [
              "2008-1359", 
              "2251-7456"
            ], 
            "name": "Proceedings - Mathematical Sciences", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "129"
          }
        ], 
        "name": "Regularity of certain diophantine equations", 
        "pagination": "19", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "afa36765d6d9c513f1347f18208ab14dd1a2b94b0cd66c2c3499686d22a94555"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s12044-019-0463-2"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1112141885"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s12044-019-0463-2", 
          "https://app.dimensions.ai/details/publication/pub.1112141885"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T13:08", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000367_0000000367/records_88230_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs12044-019-0463-2"
      }
    ]
     

    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/s12044-019-0463-2'

    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/s12044-019-0463-2'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12044-019-0463-2'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12044-019-0463-2'


     

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

    92 TRIPLES      21 PREDICATES      35 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s12044-019-0463-2 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N56f90953120d411abd152d207e1d5ff8
    4 schema:citation sg:pub.10.1007/978-3-319-68032-3_1
    5 sg:pub.10.1007/bf01188632
    6 https://doi.org/10.1016/j.disc.2017.08.040
    7 https://doi.org/10.1016/j.ejc.2017.11.008
    8 https://doi.org/10.1016/j.jcta.2005.07.004
    9 https://doi.org/10.1016/j.jcta.2009.02.009
    10 https://doi.org/10.1515/9783110925098.1
    11 https://doi.org/10.4064/aa-27-1-199-245
    12 schema:datePublished 2019-04
    13 schema:datePublishedReg 2019-04-01
    14 schema:description In Ramsey theory, there is a vast literature on regularity questions of linear diophantine equations. Some problems in higher degree have been considered recently. Here, we show that, for every pair of positive integers r and n, there exists an integer B=B(r) such that the diophantine equation ∏m=1n∑i=1kmam,ixm,i-∑j=1lmbm,jym,j=Bwith ∑i=1kmam,i=∑j=1lmbm,j∀m=1,…,nis r-regular, where km, lm are also positive integers and am,i,bm,j are non-zero integers.
    15 schema:genre non_research_article
    16 schema:inLanguage en
    17 schema:isAccessibleForFree false
    18 schema:isPartOf N2c140f21a8dc425695d6632b1cbd3477
    19 N7d596df897f74342a6f8ddbad33db715
    20 sg:journal.1320093
    21 schema:name Regularity of certain diophantine equations
    22 schema:pagination 19
    23 schema:productId N38a36606a0d0489fbffb212d508f0692
    24 N6fd0d593f83f48369222891aacdbbe01
    25 N8eab10304700482d90ab661e2ee0a993
    26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112141885
    27 https://doi.org/10.1007/s12044-019-0463-2
    28 schema:sdDatePublished 2019-04-11T13:08
    29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    30 schema:sdPublisher N84d9437d49004a4296833be7e9571d4d
    31 schema:url https://link.springer.com/10.1007%2Fs12044-019-0463-2
    32 sgo:license sg:explorer/license/
    33 sgo:sdDataset articles
    34 rdf:type schema:ScholarlyArticle
    35 N2c140f21a8dc425695d6632b1cbd3477 schema:volumeNumber 129
    36 rdf:type schema:PublicationVolume
    37 N38a36606a0d0489fbffb212d508f0692 schema:name doi
    38 schema:value 10.1007/s12044-019-0463-2
    39 rdf:type schema:PropertyValue
    40 N56f90953120d411abd152d207e1d5ff8 rdf:first Ne86debfde430419dab0d282ac684f80f
    41 rdf:rest Nd964b3b94ead4ac09d00c7e21d2efe67
    42 N6cb76bd6a1c84ce79fb47de002302699 schema:affiliation https://www.grid.ac/institutes/grid.450311.2
    43 schema:familyName Sarkar
    44 schema:givenName Subha
    45 rdf:type schema:Person
    46 N6fd0d593f83f48369222891aacdbbe01 schema:name readcube_id
    47 schema:value afa36765d6d9c513f1347f18208ab14dd1a2b94b0cd66c2c3499686d22a94555
    48 rdf:type schema:PropertyValue
    49 N7d596df897f74342a6f8ddbad33db715 schema:issueNumber 2
    50 rdf:type schema:PublicationIssue
    51 N84d9437d49004a4296833be7e9571d4d schema:name Springer Nature - SN SciGraph project
    52 rdf:type schema:Organization
    53 N8eab10304700482d90ab661e2ee0a993 schema:name dimensions_id
    54 schema:value pub.1112141885
    55 rdf:type schema:PropertyValue
    56 Nd964b3b94ead4ac09d00c7e21d2efe67 rdf:first N6cb76bd6a1c84ce79fb47de002302699
    57 rdf:rest rdf:nil
    58 Ne86debfde430419dab0d282ac684f80f schema:affiliation https://www.grid.ac/institutes/grid.450311.2
    59 schema:familyName Roy
    60 schema:givenName Bidisha
    61 rdf:type schema:Person
    62 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    63 schema:name Mathematical Sciences
    64 rdf:type schema:DefinedTerm
    65 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    66 schema:name Pure Mathematics
    67 rdf:type schema:DefinedTerm
    68 sg:journal.1320093 schema:issn 2008-1359
    69 2251-7456
    70 schema:name Proceedings - Mathematical Sciences
    71 rdf:type schema:Periodical
    72 sg:pub.10.1007/978-3-319-68032-3_1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100395159
    73 https://doi.org/10.1007/978-3-319-68032-3_1
    74 rdf:type schema:CreativeWork
    75 sg:pub.10.1007/bf01188632 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016969098
    76 https://doi.org/10.1007/bf01188632
    77 rdf:type schema:CreativeWork
    78 https://doi.org/10.1016/j.disc.2017.08.040 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091942932
    79 rdf:type schema:CreativeWork
    80 https://doi.org/10.1016/j.ejc.2017.11.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099717560
    81 rdf:type schema:CreativeWork
    82 https://doi.org/10.1016/j.jcta.2005.07.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015583004
    83 rdf:type schema:CreativeWork
    84 https://doi.org/10.1016/j.jcta.2009.02.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018714657
    85 rdf:type schema:CreativeWork
    86 https://doi.org/10.1515/9783110925098.1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1086769133
    87 rdf:type schema:CreativeWork
    88 https://doi.org/10.4064/aa-27-1-199-245 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091814301
    89 rdf:type schema:CreativeWork
    90 https://www.grid.ac/institutes/grid.450311.2 schema:alternateName Harish-Chandra Research Institute
    91 schema:name Harish-Chandra Research Institute, HBNI, Chhatnag Road, 211 019, Jhunsi, Allahabad, India
    92 rdf:type schema:Organization
     




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


    ...