{ "labelLang" : "hun", "responseDate" : "2024-03-29 10:15", "content" : { "otype" : "JournalArticle", "mtid" : 33735130, "status" : "APPROVED", "published" : true, "comment" : "Cited By :5 \n Export Date: 5 April 2023", "unhandledTickets" : 0, "deleted" : false, "lastRefresh" : "2023-04-20T11:35:36.314+0000", "lastModified" : "2023-04-20T11:34:22.517+0000", "created" : "2023-04-05T12:07:29.156+0000", "creator" : { "otype" : "Admin", "mtid" : 10084481, "link" : "/api/admin/10084481", "label" : "Toroczkai Annamária (idézők, admin)", "familyName" : "Toroczkai", "givenName" : "Annamária", "published" : true, "snippet" : true }, "lastDuplumOK" : "2023-04-20T11:34:24.031+0000", "lastDuplumSearch" : "2023-04-20T11:34:24.031+0000", "core" : false, "citation" : true, "publicationPending" : false, "type" : { "otype" : "PublicationType", "mtid" : 24, "link" : "/api/publicationtype/24", "label" : "Folyóiratcikk", "code" : 24, "otypeName" : "JournalArticle", "listPosition" : 1, "published" : true, "oldId" : 24, "snippet" : true }, "subType" : { "otype" : "SubType", "mtid" : 10000059, "link" : "/api/subtype/10000059", "label" : "Szakcikk (Folyóiratcikk)", "name" : "Szakcikk", "nameEng" : "Article", "docType" : { "otype" : "PublicationType", "mtid" : 24, "link" : "/api/publicationtype/24", "label" : "Folyóiratcikk", "code" : 24, "otypeName" : "JournalArticle", "listPosition" : 1, "published" : true, "oldId" : 24, "snippet" : true }, "listPosition" : 101, "published" : true, "oldId" : 10000059, "snippet" : true }, "category" : { "otype" : "Category", "mtid" : 1, "link" : "/api/category/1", "label" : "Tudományos", "published" : true, "oldId" : 1, "snippet" : true }, "languages" : [ { "otype" : "Language", "mtid" : 10002, "link" : "/api/language/10002", "label" : "Angol", "name" : "Angol", "nameEng" : "English", "published" : true, "oldId" : 2, "snippet" : true } ], "firstAuthor" : "Bishnoi, A.", "authorships" : [ { "otype" : "PersonAuthorship", "mtid" : 107257274, "link" : "/api/authorship/107257274", "label" : "Bishnoi, A.", "listPosition" : 1, "share" : 0.33333334, "first" : true, "last" : false, "corresponding" : false, "familyName" : "Bishnoi", "givenName" : "A.", "authorTyped" : true, "editorTyped" : false, "otherTyped" : false, "type" : { "otype" : "AuthorshipType", "mtid" : 1, "link" : "/api/authorshiptype/1", "label" : "Szerző", "code" : 0, "published" : true, "oldId" : 0, "snippet" : true }, "published" : false, "snippet" : true }, { "otype" : "PersonAuthorship", "mtid" : 107257275, "link" : "/api/authorship/107257275", "label" : "Mattheus, S.", "listPosition" : 2, "share" : 0.33333334, "first" : false, "last" : false, "corresponding" : false, "familyName" : "Mattheus", "givenName" : "S.", "authorTyped" : true, "editorTyped" : false, "otherTyped" : false, "type" : { "otype" : "AuthorshipType", "mtid" : 1, "link" : "/api/authorshiptype/1", "label" : "Szerző", "code" : 0, "published" : true, "oldId" : 0, "snippet" : true }, "published" : false, "snippet" : true }, { "otype" : "PersonAuthorship", "mtid" : 107257276, "link" : "/api/authorship/107257276", "label" : "Schillewaert, J.", "listPosition" : 3, "share" : 0.33333334, "first" : false, "last" : true, "corresponding" : false, "familyName" : "Schillewaert", "givenName" : "J.", "authorTyped" : true, "editorTyped" : false, "otherTyped" : false, "type" : { "otype" : "AuthorshipType", "mtid" : 1, "link" : "/api/authorshiptype/1", "label" : "Szerző", "code" : 0, "published" : true, "oldId" : 0, "snippet" : true }, "published" : false, "snippet" : true } ], "title" : "Minimal multiple blocking sets", "identifiers" : [ { "otype" : "PublicationIdentifier", "mtid" : 23329063, "link" : "/api/publicationidentifier/23329063", "label" : "DOI: 10.37236/7810", "source" : { "otype" : "PlainSource", "mtid" : 6, "link" : "/api/publicationsource/6", "label" : "DOI", "type" : { "otype" : "PublicationSourceType", "mtid" : 10001, "link" : "/api/publicationsourcetype/10001", "label" : "DOI", "mayHaveOa" : true, "published" : true, "snippet" : true }, "name" : "DOI", "nameEng" : "DOI", "linkPattern" : "https://doi.org/@@@", "publiclyVisible" : true, "published" : true, "oldId" : 6, "snippet" : true }, "idValue" : "10.37236/7810", "realUrl" : "https://doi.org/10.37236/7810", "published" : false, "snippet" : true }, { "otype" : "PublicationIdentifier", "mtid" : 15239668, "link" : "/api/publicationidentifier/15239668", "label" : "WoS: 000456788300021", "source" : { "otype" : "PlainSource", "mtid" : 1, "link" : "/api/publicationsource/1", "label" : "WoS", "type" : { "otype" : "PublicationSourceType", "mtid" : 10003, "link" : "/api/publicationsourcetype/10003", "label" : "Indexelő adatbázis", "mayHaveOa" : false, "published" : true, "snippet" : true }, "name" : "WoS", "nameEng" : "WoS", "linkPattern" : "https://www.webofscience.com/wos/woscc/full-record/@@@", "publiclyVisible" : true, "published" : true, "oldId" : 1, "snippet" : true }, "validState" : "IDENTICAL", "idValue" : "000456788300021", "realUrl" : "https://www.webofscience.com/wos/woscc/full-record/000456788300021", "published" : false, "snippet" : true }, { "otype" : "PublicationIdentifier", "mtid" : 23329062, "link" : "/api/publicationidentifier/23329062", "label" : "Scopus: 85061613850", "source" : { "otype" : "PlainSource", "mtid" : 3, "link" : "/api/publicationsource/3", "label" : "Scopus", "type" : { "otype" : "PublicationSourceType", "mtid" : 10003, "link" : "/api/publicationsourcetype/10003", "label" : "Indexelő adatbázis", "mayHaveOa" : false, "published" : true, "snippet" : true }, "name" : "Scopus", "linkPattern" : "http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@", "publiclyVisible" : true, "published" : true, "oldId" : 3, "snippet" : true }, "idValue" : "85061613850", "realUrl" : "http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85061613850", "published" : false, "snippet" : true } ], "journal" : { "otype" : "Journal", "mtid" : 10003114, "link" : "/api/journal/10003114", "label" : "ELECTRONIC JOURNAL OF COMBINATORICS 1097-1440 1077-8926", "pIssn" : "1097-1440", "eIssn" : "1077-8926", "reviewType" : "REVIEWED", "noIF" : false, "sciIndexed" : true, "scopusIndexed" : true, "lang" : "FOREIGN", "hungarian" : false, "published" : true, "oldId" : 10003114, "snippet" : true }, "volume" : "25", "issue" : "4", "internalId" : "#P4.66", "firstPageOrInternalIdForSort" : "#P4.66", "publishedYear" : 2018, "abstractText" : "We prove that a minimal t-fold blocking set in a finite projective plane of order n has cardinality at most (Formula presented) This is the first general upper bound on the size of minimal t-fold blocking sets in finite projective planes and it generalizes the classical result of Bruen and Thas on minimal blocking sets. From the proof it directly follows that if equality occurs in this bound then every line intersects the blocking set S in either t points or (Formula presented) points. We use this to show that for n a prime power, equality can occur in our bound in exactly one of the√ following three cases: (a) t = 1, n is a square and S is a unital; (b) t = n − √n, n is a square and S is the complement of a Baer subplane; (c) t = n and S is√ equal to the set of all points except one. For a square prime power q and t √q + 1, we√ give a construction√ of a minimal t-fold blocking set S in PG(2, q) with |S| = q q + 1 + (t − 1)(q − √q + 1). Furthermore, we obtain an upper bound on the size of minimal blocking sets in symmetric 2-designs and use it to give new proofs of other known results regarding tangency sets in higher dimensional finite projective spaces. We also discuss further generalizations of our bound. In our proofs we use an incidence bound on combinatorial designs which follows from applying the expander mixing lemma to the incidence graph of these designs. © The authors.", "digital" : true, "printed" : false, "sourceYear" : 2023, "foreignEdition" : true, "foreignLanguage" : true, "fullPublication" : true, "conferencePublication" : false, "nationalOrigin" : false, "missingAuthor" : false, "oaType" : "GOLD", "oaCheckDate" : "2023-04-20", "oaFree" : false, "oaLink" : "http://www.combinatorics.org/index.html", "citationCount" : 0, "citationCountUnpublished" : 0, "citationCountWoOther" : 0, "independentCitCountWoOther" : 0, "doiCitationCount" : 0, "wosCitationCount" : 0, "scopusCitationCount" : 0, "independentCitationCount" : 0, "unhandledCitationCount" : 0, "citingPubCount" : 0, "independentCitingPubCount" : 0, "unhandledCitingPubCount" : 0, "citedPubCount" : 4, "citedCount" : 4, "ratings" : [ { "otype" : "SjrRating", "mtid" : 10742306, "link" : "/api/sjrrating/10742306", "label" : "sjr:Q2 (2018) Scopus - Applied Mathematics ELECTRONIC JOURNAL OF COMBINATORICS 1097-1440 1077-8926", "listPos" : 149, "rankValue" : 0.49, "type" : "journal", "ratingType" : { "otype" : "RatingType", "mtid" : 10002, "link" : "/api/ratingtype/10002", "label" : "sjr", "code" : "sjr", "published" : true, "snippet" : true }, "subject" : { "otype" : "ClassificationExternal", "mtid" : 2604, "link" : "/api/classificationexternal/2604", "label" : "Scopus - Applied Mathematics", "published" : true, "oldId" : 2604, "snippet" : true }, "ranking" : "Q2", "calculation" : "DIRECT", "published" : true, "snippet" : true } ], "ratingsForSort" : "Q2", "references" : [ { "otype" : "Reference", "mtid" : 39910431, "link" : "/api/reference/39910431", "label" : "1. Baer, R., Polarities in finite projective planes (1946) Bull. Amer. Math. Soc., 52, pp. 77-93", "listPosition" : 1, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910432, "link" : "/api/reference/39910432", "label" : "2. Ball, S., Multiple blocking sets and arcs in finite planes (1996) J. London Math. Soc., 54, pp. 581-593", "listPosition" : 2, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910433, "link" : "/api/reference/39910433", "label" : "3. Ball, S., On small complete arcs in a finite plane (1997) Discrete Math, 174, pp. 29-34", "listPosition" : 3, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910434, "link" : "/api/reference/39910434", "label" : "4. Ball, S., Finite Geometry and Combinatorial Applications, volume 82 of London Mathematical Society Student Texts (2015) Cambridge Univ. Press, Cambridge", "listPosition" : 4, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910435, "link" : "/api/reference/39910435", "label" : "5. Barwick, S., Ebert, G., (2008), and. Unitals in Projective Planes. Springer", "listPosition" : 5, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910436, "link" : "/api/reference/39910436", "label" : "6. Blokhuis, A., Blocking sets in Desarguesian planes (1996) Combinatorics: Paul Erdős is Eighty, Vol. 2, Pages 133–155. Bolyai Soc. Math. Stud", "listPosition" : 6, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910437, "link" : "/api/reference/39910437", "label" : "7. Blokhuis, A., Eric Moorhouse, G., Some p-Ranks Related to Orthogonal Spaces (1995) J. Algeb. Combin., 4, pp. 295-316", "listPosition" : 7, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910438, "link" : "/api/reference/39910438", "label" : "8. Blokhuis, A., Sziklai, P., Szőnyi, T., Blocking sets in projective spaces (2011) Current Research Topics on Galois Geometry, pp. 61-84. , J. De Beule and L. Storme (eds.), pages, Nova Academic Publishers", "listPosition" : 8, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910439, "link" : "/api/reference/39910439", "label" : "9. Brouwer, A.E., Haemers, W., (2012) Spectra of Graphs, , Springer", "listPosition" : 9, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910440, "link" : "/api/reference/39910440", "label" : "10. Bruen, A.A., Drudge, K., The return of the Baer subplane (1999) J. Comb. Theory Ser. A, 85, pp. 228-231", "listPosition" : 10, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910441, "link" : "/api/reference/39910441", "label" : "11. Bruen, A.A., Thas, J.A., Blocking sets (1977) Geom. Dedicata, 6, pp. 193-203", "listPosition" : 11, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910442, "link" : "/api/reference/39910442", "label" : "12. Bruen, A.A., Thas, J.A., Hyperplane coverings and blocking sets (1982) Math. Z., 181, pp. 407-409", "listPosition" : 12, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910443, "link" : "/api/reference/39910443", "label" : "13. Bruen, A.A., Arcs and multiple blocking sets (1986) Combinatoria, Symposia Mathematica, 28, pp. 15-29", "listPosition" : 13, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910444, "link" : "/api/reference/39910444", "label" : "14. Csajbók, B., Kiss, G., Notes on semiarcs (2012) Mediterr. J. Math., 9, pp. 677-692", "listPosition" : 14, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910445, "link" : "/api/reference/39910445", "label" : "15. de Finis, M., (1981) On K-Sets of Type (M, N) in Projective Planes of Square Order, Pages 98–103. London Mathematical Society Lecture Note Series, , Cambridge University Press", "listPosition" : 15, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910446, "link" : "/api/reference/39910446", "label" : "16. de Winter, S., Schillewaert, J., Verstraete, J., Large incidence-free sets in geometries (2012) Electron. J. Combin, 19 (4), p. 24", "listPosition" : 16, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910447, "link" : "/api/reference/39910447", "label" : "17. Dembowski, P., (1997) Finite Geometries: Reprint of The, , 1968 edition., Springer", "listPosition" : 17, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910448, "link" : "/api/reference/39910448", "label" : "18. Haemers, W.H., Interlacing eigenvalues and graphs (1995) Linear Algebra Appl, 226 (616)", "listPosition" : 18, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910449, "link" : "/api/reference/39910449", "label" : "19. Hughes, D., Piper, F., Projective Planes. Graduate Texts in Mathematics, 6. , Springer-Verlag, New York-Berlin, 1973. x+291 pp", "listPosition" : 19, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910450, "link" : "/api/reference/39910450", "label" : "20. Hoory, S., Linial, N., Wigderson, A., Expander graphs and their applications (2006) Bull. Am. Math. Soc, 43, pp. 439-561", "listPosition" : 20, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910451, "link" : "/api/reference/39910451", "label" : "21. Kim, J., Vu, V., Small complete arcs in projective planes (2003) Combinatorica, 23 (2), pp. 311-363. , no", "listPosition" : 21, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910452, "link" : "/api/reference/39910452", "label" : "22. Lund, B., Saraf, S., Incidence bounds for block designs (2016) SIAM J. Discrete Math., 30, pp. 1997-2010", "listPosition" : 22, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910453, "link" : "/api/reference/39910453", "label" : "23. Lund, B., Saraf, S., Wolf, C., (2016) Finite Field Kakeya and Nikodym Sets in Three Dimensions, , arXiv", "listPosition" : 23, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910454, "link" : "/api/reference/39910454", "label" : "24. Murphy, B., Petridis, G., A point-line incidence identity in finite fields, and applications (2016) Moscow Journal of Combinatorics and Number Theory, 6, pp. 64-95", "listPosition" : 24, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910455, "link" : "/api/reference/39910455", "label" : "25. Penttila, T., Royle, G., Sets of type (M, n) in the affine and projective planes of order nine (1995) Des. Codes Cryptogr., 6, pp. 229-245", "listPosition" : 25, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910456, "link" : "/api/reference/39910456", "label" : "26. Seib, M., Unitäre Polaritäten endlicher projektiver Ebenen (1970) German) Arch. Math., 21, pp. 103-112", "listPosition" : 26, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910457, "link" : "/api/reference/39910457", "label" : "27. Illés, T., Szőnyi, T., Wettl, F., Maximal strong representative systems and minimal blocking sets. Mitt (1991) Math. Sem. Giessen, 201, pp. 97-107", "listPosition" : 27, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910458, "link" : "/api/reference/39910458", "label" : "28. Szőnyi, T., Note on the existence of large minimal blocking sets in Galois planes (1992) Combinatorica, 12, pp. 227-235", "listPosition" : 28, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910459, "link" : "/api/reference/39910459", "label" : "29. Szőnyi, T., Cossidente, A., Gács, A., Mengyán, C., Siciliano, A., Weiner, Z., On large minimal blocking sets in PG(2, q) (2005) J. Combin. Designs, 13, pp. 25-41", "listPosition" : 29, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910460, "link" : "/api/reference/39910460", "label" : "30. Tallini, G., Some new results on sets of type (M, n) in projective planes (1987) J. Geom., 29, pp. 191-199", "listPosition" : 30, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910461, "link" : "/api/reference/39910461", "label" : "31. Thas, J.A., On semi ovals and semi ovoids (1974) Geom. Dedicata, 3, pp. 229-231", "listPosition" : 31, "published" : false, "snippet" : true }, { "otype" : "Reference", "mtid" : 39910462, "link" : "/api/reference/39910462", "label" : "32. Vinh, L.A., The Szemerédi-Trotter type theorem and the sum-product estimate in finite fields (2011) European J. Combin., 32, pp. 1177-1181", "listPosition" : 32, "published" : false, "snippet" : true } ], "hasCitationDuplums" : false, "userChangeableUntil" : "2023-07-04T12:09:03.635+0000", "directInstitutesForSort" : "", "ownerAuthorCount" : 6, "ownerInstituteCount" : 12, "directInstituteCount" : 0, "authorCount" : 3, "contributorCount" : 0, "hasQualityFactor" : true, "link" : "/api/publication/33735130", "label" : "Bishnoi A. et al. Minimal multiple blocking sets. (2018) ELECTRONIC JOURNAL OF COMBINATORICS 1097-1440 1077-8926 25 4", "template" : "