{"id":"https://openalex.org/W4406950649","doi":"https://doi.org/10.1007/s00493-025-00193-9","title":"Multiplicative irreducibility of small perturbations of the set of shifted k-th powers","display_name":"Multiplicative irreducibility of small perturbations of the set of shifted k-th powers","publication_year":2026,"publication_date":"2026-01-07","ids":{"openalex":"https://openalex.org/W4406950649","doi":"https://doi.org/10.1007/s00493-025-00193-9"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-025-00193-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00193-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00193-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00193-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061055178","display_name":"Chi Hoi Yip","orcid":"https://orcid.org/0000-0003-0753-1675"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chi Hoi Yip","raw_affiliation_strings":["School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, United States","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5061055178"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":18.4204,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.96932169,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"46","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9911999702453613,"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":0.9911999702453613,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9775999784469604,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9635999798774719,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/irreducibility","display_name":"Irreducibility","score":0.9691464900970459},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49534860253334045},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.34481221437454224},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32406407594680786}],"concepts":[{"id":"https://openalex.org/C2776823524","wikidata":"https://www.wikidata.org/wiki/Q6073561","display_name":"Irreducibility","level":2,"score":0.9691464900970459},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49534860253334045},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.34481221437454224},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32406407594680786}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00493-025-00193-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00193-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00193-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2501.16620","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2501.16620","pdf_url":"https://arxiv.org/pdf/2501.16620","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2501.16620","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2501.16620","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":"doi:10.1007/s00493-025-00193-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00193-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00193-9.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4406950649.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W4410616813","https://openalex.org/W4383372113","https://openalex.org/W2052995846","https://openalex.org/W1567822258","https://openalex.org/W1548337223","https://openalex.org/W4399400347","https://openalex.org/W68891353","https://openalex.org/W1974065123","https://openalex.org/W4239450633","https://openalex.org/W4240413003","https://openalex.org/W2789616721","https://openalex.org/W3011473838","https://openalex.org/W1444168583","https://openalex.org/W2060986573","https://openalex.org/W2483116445","https://openalex.org/W2962798712","https://openalex.org/W4406228052","https://openalex.org/W4407663211"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1630580488","https://openalex.org/W2007170860","https://openalex.org/W4319349750","https://openalex.org/W2951407429","https://openalex.org/W4246385323","https://openalex.org/W2145139444","https://openalex.org/W4383993686","https://openalex.org/W4379981171","https://openalex.org/W2229306178"],"abstract_inverted_index":{"Abstract":[0],"Motivated":[1],"by":[2],"a":[3,24,115,125],"conjecture":[4,29,131],"of":[5,11,14,17,27,72,129],"Erd\u0151s":[6],"on":[7],"the":[8,15,28,108],"additive":[9],"irreducibility":[10],"small":[12],"perturbations":[13],"set":[16,110,117],"squares,":[18],"recently":[19],"Hajdu":[20],"and":[21],"S\u00e1rk\u00f6zy":[22],"studied":[23],"multiplicative":[25],"analogue":[26],"for":[30,38,132],"shifted":[31],"k":[32],"-th":[33],"powers.":[34],"They":[35],"conjectured":[36],"that":[37],"each":[39],"$$k\\ge":[40,133],"2$$":[41],"<mml:math":[42,55,78,135],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[43,56,79,136],"<mml:mrow>":[44,57,62,80,87,137],"<mml:mi>k</mml:mi>":[45,65,83,91,138],"<mml:mo>\u2265</mml:mo>":[46,139],"<mml:mn>2</mml:mn>":[47],"</mml:mrow>":[48,66,69,100,101,141],"</mml:math>":[49,70,102,142],",":[50,106],"if":[51],"one":[52],"changes":[53],"$$o(X^{1/k})$$":[54],"<mml:mi>o</mml:mi>":[58],"<mml:mo>(</mml:mo>":[59],"<mml:msup>":[60,89],"<mml:mi>X</mml:mi>":[61],"<mml:mn>1</mml:mn>":[63,94],"<mml:mo>/</mml:mo>":[64],"</mml:msup>":[67,92],"<mml:mo>)</mml:mo>":[68],"elements":[71],"$$M_k'=\\{x^k+1:":[73],"x":[74],"\\in":[75],"\\mathbb":[76],"{N}\\}$$":[77],"<mml:msubsup>":[81],"<mml:mi>M</mml:mi>":[82],"<mml:mo>\u2032</mml:mo>":[84],"</mml:msubsup>":[85],"<mml:mo>=</mml:mo>":[86],"<mml:mo>{</mml:mo>":[88],"<mml:mi>x</mml:mi>":[90,96],"<mml:mo>+</mml:mo>":[93],"<mml:mo>:</mml:mo>":[95],"<mml:mo>\u2208</mml:mo>":[97],"<mml:mi>N</mml:mi>":[98],"<mml:mo>}</mml:mo>":[99],"up":[103],"to":[104],"X":[105],"then":[107],"resulting":[109],"cannot":[111],"be":[112],"written":[113],"as":[114],"product":[116],"AB":[118],"nontrivially.":[119],"In":[120],"this":[121],"paper,":[122],"we":[123],"confirm":[124],"more":[126],"general":[127],"version":[128],"their":[130],"3$$":[134],"<mml:mn>3</mml:mn>":[140],".":[143]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-01-30T00:00:00"}