{"id":"https://openalex.org/W2146983136","doi":"https://doi.org/10.37236/1510","title":"Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers","display_name":"Symmetric Sum-Free Partitions and Lower Bounds for Schur Numbers","publication_year":2000,"publication_date":"2000-05-18","ids":{"openalex":"https://openalex.org/W2146983136","doi":"https://doi.org/10.37236/1510","mag":"2146983136"},"language":"en","primary_location":{"id":"doi:10.37236/1510","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1510","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r32/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044041262","display_name":"Harold Fredricksen","orcid":null},"institutions":[{"id":"https://openalex.org/I3149230897","display_name":"Institute For Defense Analyses","ror":"https://ror.org/00rh8m666","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I3149230897"]},{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]},{"id":"https://openalex.org/I4210157118","display_name":"CCI Reprographics (United States)","ror":"https://ror.org/04d7j1v83","country_code":"US","type":"company","lineage":["https://openalex.org/I4210157118"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Harold Fredricksen","raw_affiliation_strings":["Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121, USA","Naval Postgraduate School,","Institute for Defense Analyses,","Department of Mathematics, Monterey, CA 93943, USA"],"affiliations":[{"raw_affiliation_string":"Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121, USA","institution_ids":["https://openalex.org/I4210157118"]},{"raw_affiliation_string":"Naval Postgraduate School,","institution_ids":["https://openalex.org/I35364215"]},{"raw_affiliation_string":"Institute for Defense Analyses,","institution_ids":["https://openalex.org/I3149230897"]},{"raw_affiliation_string":"Department of Mathematics, Monterey, CA 93943, USA","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066514608","display_name":"Melvin M. Sweet","orcid":null},"institutions":[{"id":"https://openalex.org/I35364215","display_name":"Naval Postgraduate School","ror":"https://ror.org/033yfkj90","country_code":"US","type":"education","lineage":["https://openalex.org/I1330347796","https://openalex.org/I3130687028","https://openalex.org/I35364215"]},{"id":"https://openalex.org/I3149230897","display_name":"Institute For Defense Analyses","ror":"https://ror.org/00rh8m666","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I3149230897"]},{"id":"https://openalex.org/I4210157118","display_name":"CCI Reprographics (United States)","ror":"https://ror.org/04d7j1v83","country_code":"US","type":"company","lineage":["https://openalex.org/I4210157118"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Melvin M. Sweet","raw_affiliation_strings":["Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121, USA","Department of Mathematics, Monterey, CA 93943, USA","Institute for Defense Analyses,","Naval Postgraduate School,"],"affiliations":[{"raw_affiliation_string":"Center for Communications Research, 4320 Westerra Court, San Diego, CA 92121, USA","institution_ids":["https://openalex.org/I4210157118"]},{"raw_affiliation_string":"Department of Mathematics, Monterey, CA 93943, USA","institution_ids":[]},{"raw_affiliation_string":"Institute for Defense Analyses,","institution_ids":["https://openalex.org/I3149230897"]},{"raw_affiliation_string":"Naval Postgraduate School,","institution_ids":["https://openalex.org/I35364215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5066514608"],"corresponding_institution_ids":["https://openalex.org/I3149230897","https://openalex.org/I35364215","https://openalex.org/I4210157118"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.27204503,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"7","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9980999827384949,"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"}},{"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8504809737205505},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8281410932540894},{"id":"https://openalex.org/keywords/schur-polynomial","display_name":"Schur polynomial","score":0.5117464065551758},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4964943528175354},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.4433932900428772},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36418843269348145},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.08066335320472717}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8504809737205505},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8281410932540894},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.5117464065551758},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4964943528175354},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.4433932900428772},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36418843269348145},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.08066335320472717},{"id":"https://openalex.org/C86607863","wikidata":"https://www.wikidata.org/wiki/Q5275279","display_name":"Difference polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1510","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1510","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.95.907","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.95.907","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_7/PDF/v7i1r32.pdf","raw_type":"text"},{"id":"pmh:oai:calhoun.nps.edu:10945/40329","is_oa":false,"landing_page_url":"http://hdl.handle.net/10945/40329","pdf_url":null,"source":{"id":"https://openalex.org/S4306400952","display_name":"Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I35364215","host_organization_name":"Naval Postgraduate School","host_organization_lineage":["https://openalex.org/I35364215"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/1510","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1510","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2146983136.pdf","grobid_xml":"https://content.openalex.org/works/W2146983136.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W50207286","https://openalex.org/W1604945782","https://openalex.org/W2037407030","https://openalex.org/W2082214688","https://openalex.org/W2105497083","https://openalex.org/W2295268496"],"related_works":["https://openalex.org/W2917894457","https://openalex.org/W4288555406","https://openalex.org/W4282813460","https://openalex.org/W2950553984","https://openalex.org/W4289303731","https://openalex.org/W2989804646","https://openalex.org/W2899663113","https://openalex.org/W2134984950","https://openalex.org/W4387355916","https://openalex.org/W2969989209"],"abstract_inverted_index":{"We":[0,26],"give":[1],"new":[2,15],"lower":[3,16],"bounds":[4,17],"for":[5,18],"the":[6,19],"Schur":[7],"numbers":[8],"$S(6)$":[9],"and":[10,24],"$S(7)$.":[11],"This":[12],"will":[13],"imply":[14],"Multicolor":[20],"Ramsey":[21],"Numbers":[22],"$R_6(3)$":[23],"$R_7(3)$.":[25],"also":[27],"make":[28],"several":[29],"observations":[30],"concerning":[31],"symmetric":[32],"sum-free":[33],"partitions":[34],"into":[35],"5":[36],"sets.":[37]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}