{"id":"https://openalex.org/W4406843654","doi":"https://doi.org/10.3390/sym17020179","title":"Symmetric Point Sets with Few Intersection Numbers in PG(r,q)","display_name":"Symmetric Point Sets with Few Intersection Numbers in PG(r,q)","publication_year":2025,"publication_date":"2025-01-24","ids":{"openalex":"https://openalex.org/W4406843654","doi":"https://doi.org/10.3390/sym17020179"},"language":"en","primary_location":{"id":"doi:10.3390/sym17020179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020179","pdf_url":"https://www.mdpi.com/2073-8994/17/2/179/pdf?version=1737732352","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/2/179/pdf?version=1737732352","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037924959","display_name":"Stefano Innamorati","orcid":"https://orcid.org/0000-0002-6109-6566"},"institutions":[{"id":"https://openalex.org/I26415053","display_name":"University of L'Aquila","ror":"https://ror.org/01j9p1r26","country_code":"IT","type":"education","lineage":["https://openalex.org/I26415053"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Stefano Innamorati","raw_affiliation_strings":["Department of Industrial and Information Engineering and Economic, University of L\u2019Aquila, Piazzale Ernesto Pontieri, 1, I-67100 L\u2019Aquila, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Industrial and Information Engineering and Economic, University of L\u2019Aquila, Piazzale Ernesto Pontieri, 1, I-67100 L\u2019Aquila, Italy","institution_ids":["https://openalex.org/I26415053"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037924959"],"corresponding_institution_ids":["https://openalex.org/I26415053"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.4617,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.88038032,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"17","issue":"2","first_page":"179","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9869999885559082,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7214094400405884},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5600061416625977},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5423098802566528},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4561154544353485},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1482999622821808},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.03894317150115967}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7214094400405884},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5600061416625977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5423098802566528},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4561154544353485},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1482999622821808},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.03894317150115967},{"id":"https://openalex.org/C58640448","wikidata":"https://www.wikidata.org/wiki/Q42515","display_name":"Cartography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym17020179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020179","pdf_url":"https://www.mdpi.com/2073-8994/17/2/179/pdf?version=1737732352","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:mdpi.com:/2073-8994/17/2/179/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym17020179","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pages: 179","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym17020179","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020179","pdf_url":"https://www.mdpi.com/2073-8994/17/2/179/pdf?version=1737732352","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406843654.pdf","grobid_xml":"https://content.openalex.org/works/W4406843654.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1512977550","https://openalex.org/W1591242241","https://openalex.org/W1964043652","https://openalex.org/W1973483608","https://openalex.org/W1974773774","https://openalex.org/W2027062106","https://openalex.org/W2030243808","https://openalex.org/W2073965660","https://openalex.org/W2080856338","https://openalex.org/W2084976617","https://openalex.org/W2124113125","https://openalex.org/W2473381345","https://openalex.org/W3159373312","https://openalex.org/W3179956273","https://openalex.org/W4243644698","https://openalex.org/W4390454565","https://openalex.org/W4399364785","https://openalex.org/W6720798715","https://openalex.org/W6806365156"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W1977169298","https://openalex.org/W2371953206","https://openalex.org/W2382500641","https://openalex.org/W4230797523","https://openalex.org/W2801497733"],"abstract_inverted_index":{"In":[0,22],"1965,":[1],"H.":[2],"Retkin":[3],"and":[4,54,74,77],"E.":[5],"Stein":[6],"defined":[7],"a":[8,13,27],"symmetric":[9,31,45,106,124],"point":[10,32,107],"set":[11,14],"as":[12],"of":[15,30,34,44,64,88],"points":[16],"with":[17,95,109,126],"the":[18,35,42,62,68,85],"same":[19],"intersection":[20,99,111,128],"numbers.":[21,129],"this":[23],"paper,":[24],"we":[25],"perform":[26],"detailed":[28],"analysis":[29],"sets":[33,46,53,71,76,108,125],"finite":[36,120],"projective":[37,121],"space":[38,122],"which":[39,90],"shows":[40],"that":[41,118],"class":[43],"is":[47],"very":[48],"broad":[49],"including":[50],"caps,":[51,94],"two-character":[52,75],"transitive":[55],"sets.":[56,66],"We":[57],"derive":[58],"necessary":[59],"conditions":[60],"for":[61],"existence":[63],"such":[65],"Since":[67],"most":[69],"studied":[70],"are":[72,91,113],"caps":[73],"not":[78],"much":[79],"seems":[80],"to":[81],"be":[82],"known":[83],"in":[84],"general":[86],"case":[87],"sets,":[89],"different":[92],"from":[93],"more":[96],"than":[97],"two":[98],"numbers,":[100],"by":[101],"using":[102],"incidence-preserving":[103],"group":[104],"actions,":[105],"few":[110,127],"numbers":[112],"provided.":[114],"The":[115],"results":[116],"indicate":[117],"any":[119],"contains":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-04-01T17:29:45.350535","created_date":"2025-10-10T00:00:00"}