{"id":"https://openalex.org/W2783205753","doi":"https://doi.org/10.1007/s00493-019-3933-3","title":"Waring\u2019s Theorem for Binary Powers","display_name":"Waring\u2019s Theorem for Binary Powers","publication_year":2019,"publication_date":"2019-10-29","ids":{"openalex":"https://openalex.org/W2783205753","doi":"https://doi.org/10.1007/s00493-019-3933-3","mag":"2783205753"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-019-3933-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-019-3933-3","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.04483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035962853","display_name":"Daniel M. Kane","orcid":"https://orcid.org/0000-0002-0220-9962"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel M. Kane","raw_affiliation_strings":["Mathematics University of California, San Diego, 9500 Gilman Drive #0404, La Jolla, CA, 92093-0404, USA","Mathematics University of California, San Diego, La Jolla, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics University of California, San Diego, 9500 Gilman Drive #0404, La Jolla, CA, 92093-0404, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"Mathematics University of California, San Diego, La Jolla, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030500922","display_name":"Carlo Sanna","orcid":"https://orcid.org/0000-0002-2111-7596"},"institutions":[{"id":"https://openalex.org/I55143463","display_name":"University of Turin","ror":"https://ror.org/048tbm396","country_code":"IT","type":"education","lineage":["https://openalex.org/I55143463"]},{"id":"https://openalex.org/I1330701686","display_name":"Collegio Carlo Alberto","ror":"https://ror.org/0397knh37","country_code":"IT","type":"education","lineage":["https://openalex.org/I1330701686"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo Sanna","raw_affiliation_strings":["Dipartimento di Matematica \u201cGiuseppe Peano\u201d, Universit\u00e0 degli Studi di Torino, Via Carlo Alberto 10, 10123, Torino, Italy","Dipartimento di Matematica \u201cGiuseppe Peano\u201d, Universit\u00e0 degli Studi di Torino, Torino, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cGiuseppe Peano\u201d, Universit\u00e0 degli Studi di Torino, Via Carlo Alberto 10, 10123, Torino, Italy","institution_ids":["https://openalex.org/I1330701686","https://openalex.org/I55143463"]},{"raw_affiliation_string":"Dipartimento di Matematica \u201cGiuseppe Peano\u201d, Universit\u00e0 degli Studi di Torino, Torino, Italy","institution_ids":["https://openalex.org/I55143463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065322269","display_name":"Jeffrey Shallit","orcid":"https://orcid.org/0000-0003-1197-3820"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Jeffrey Shallit","raw_affiliation_strings":["School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","School of Computer Science,, University of Waterloo, Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"School of Computer Science,, University of Waterloo, Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035962853"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03928457,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"6","first_page":"1335","last_page":"1350"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994000196456909,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9994000196456909,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.9990000128746033,"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/binary-number","display_name":"Binary number","score":0.8336030840873718},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.8231062889099121},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7598661780357361},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7123382687568665},{"id":"https://openalex.org/keywords/sums-of-powers","display_name":"Sums of powers","score":0.5190958976745605},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5187497138977051},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.4357263743877411},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.43099355697631836},{"id":"https://openalex.org/keywords/power-of-two","display_name":"Power of two","score":0.4264104664325714},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18642708659172058},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.09844905138015747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.078073650598526}],"concepts":[{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.8336030840873718},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8231062889099121},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7598661780357361},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7123382687568665},{"id":"https://openalex.org/C46221946","wikidata":"https://www.wikidata.org/wiki/Q15051202","display_name":"Sums of powers","level":2,"score":0.5190958976745605},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5187497138977051},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.4357263743877411},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.43099355697631836},{"id":"https://openalex.org/C7720571","wikidata":"https://www.wikidata.org/wiki/Q1136880","display_name":"Power of two","level":2,"score":0.4264104664325714},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18642708659172058},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.09844905138015747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.078073650598526},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00493-019-3933-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-019-3933-3","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1801.04483","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.04483","pdf_url":"https://arxiv.org/pdf/1801.04483","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2783205753","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.04483.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:escholarship.org/ark:/13030/qt4zf7g1vw","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/4zf7g1vw","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"COMBINATORICA, vol 39, iss 6","raw_type":"article"},{"id":"doi:10.48550/arxiv.1801.04483","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.04483","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1801.04483","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.04483","pdf_url":"https://arxiv.org/pdf/1801.04483","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4181904149","display_name":null,"funder_award_id":"105829/2013","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G6671297155","display_name":null,"funder_award_id":"CAREER","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2783205753.pdf","grobid_xml":"https://content.openalex.org/works/W2783205753.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1495204714","https://openalex.org/W1568671078","https://openalex.org/W2014581752","https://openalex.org/W2016090591","https://openalex.org/W2316633611","https://openalex.org/W2332901121","https://openalex.org/W2479604145","https://openalex.org/W2604824373","https://openalex.org/W2611564954","https://openalex.org/W2752853835","https://openalex.org/W2767147153","https://openalex.org/W2790140360","https://openalex.org/W2890439620","https://openalex.org/W2895696152","https://openalex.org/W2963605982","https://openalex.org/W2964257454","https://openalex.org/W4205562629","https://openalex.org/W4245603972","https://openalex.org/W6608815102"],"related_works":["https://openalex.org/W2982669126","https://openalex.org/W3098902506","https://openalex.org/W2027626405","https://openalex.org/W2064864727","https://openalex.org/W2085169541","https://openalex.org/W2518555084","https://openalex.org/W2010902044","https://openalex.org/W3122615737","https://openalex.org/W2953277056","https://openalex.org/W3133519977","https://openalex.org/W3212818577","https://openalex.org/W1806292777","https://openalex.org/W2950040968","https://openalex.org/W2765622810","https://openalex.org/W2883920223","https://openalex.org/W2596966949","https://openalex.org/W2536700725","https://openalex.org/W3127222588","https://openalex.org/W2962902758","https://openalex.org/W2903993041"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}