{"id":"https://openalex.org/W4414262736","doi":"https://doi.org/10.5070/c65365553","title":"On the determination of sets by their subset sums","display_name":"On the determination of sets by their subset sums","publication_year":2025,"publication_date":"2025-09-12","ids":{"openalex":"https://openalex.org/W4414262736","doi":"https://doi.org/10.5070/c65365553"},"language":"en","primary_location":{"id":"doi:10.5070/c65365553","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65365553","pdf_url":"https://escholarship.org/content/qt9s01w2p2/qt9s01w2p2.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt9s01w2p2/qt9s01w2p2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037543212","display_name":"Andrea Ciprietti","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrea Ciprietti","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001839288","display_name":"Federico Glaudo","orcid":"https://orcid.org/0009-0004-1243-0515"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Federico Glaudo","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037543212"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.37601403,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.4507000148296356,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.4507000148296356,"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"}},{"id":"https://openalex.org/T13257","display_name":"Advanced Control and Stabilization in Aerospace Systems","score":0.4153999984264374,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/abelian-group","display_name":"Abelian group","score":0.7821999788284302},{"id":"https://openalex.org/keywords/multiplicative-group","display_name":"Multiplicative group","score":0.6348999738693237},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.6337000131607056},{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.5946000218391418},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5461000204086304},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.42570000886917114},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.3743000030517578},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.3490999937057495}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8454999923706055},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7821999788284302},{"id":"https://openalex.org/C92788228","wikidata":"https://www.wikidata.org/wiki/Q3777923","display_name":"Multiplicative group","level":3,"score":0.6348999738693237},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.6337000131607056},{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.5946000218391418},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5461000204086304},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5267999768257141},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45329999923706055},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.42570000886917114},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.3490999937057495},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.3407999873161316},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3382999897003174},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3353999853134155},{"id":"https://openalex.org/C154441711","wikidata":"https://www.wikidata.org/wiki/Q1782332","display_name":"Divisible group","level":5,"score":0.3019999861717224},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.26739999651908875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2671000063419342},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5070/c65365553","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65365553","pdf_url":"https://escholarship.org/content/qt9s01w2p2/qt9s01w2p2.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:doi:10.5070/C65365553","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S7407050878","display_name":"California Digital Library","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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/journal article"}],"best_oa_location":{"id":"doi:10.5070/c65365553","is_oa":true,"landing_page_url":"https://doi.org/10.5070/c65365553","pdf_url":"https://escholarship.org/content/qt9s01w2p2/qt9s01w2p2.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4414262736.pdf"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0,11],"\\(A\\)":[1],"be":[2,13,127],"a":[3,46,72,80,97,108,116],"multiset":[4,15],"with":[5],"elements":[6],"in":[7],"an":[8,112],"abelian":[9,77,123],"group.":[10],"\\(\\operatorname{FS}(A)\\)":[12],"the":[14,17,27,50,59,76,85,93,101],"containing":[16],"\\(2^{|A|}\\)":[18],"sums":[19],"of":[20,23,71,75,92,100,103,128],"all":[21],"subsets":[22],"\\(A\\).":[24],"We":[25,38],"study":[26,99],"reconstruction":[28,60],"problem":[29,61],"\"Given":[30],"\\(\\operatorname{FS}(A)\\),":[31],"is":[32,55,62],"it":[33],"possible":[34],"to":[35,42,84],"identify":[36],"\\(A\\)?\".":[37],"prove":[39],"that,":[40],"up":[41],"identifying":[43],"multisets":[44],"through":[45],"natural":[47],"equivalence":[48],"relation,":[49],"function":[51],"\\(A":[52],"\\mapsto":[53],"\\operatorname{FS}(A)\\)":[54],"injective":[56],"(and":[57],"thus":[58],"solvable)":[63],"if":[64,67],"and":[65],"only":[66],"every":[68],"order":[69],"\\(n\\)":[70],"torsion":[73],"element":[74],"group":[78,87],"satisfies":[79],"number-theoretical":[81],"property":[82],"related":[83],"multiplicative":[86],"\\((\\mathbb{Z}/n":[88],"\\mathbb{Z})^*\\).":[89],"The":[90],"core":[91],"proof":[94],"relies":[95],"on":[96,121],"delicate":[98],"structure":[102],"cyclotomic":[104,143],"units.":[105],"Moreover,":[106],"as":[107],"tool,":[109],"we":[110],"develop":[111],"inversion":[113],"formula":[114],"for":[115],"novel":[117],"discrete":[118],"Radon":[119,141],"transform":[120],"finite":[122],"groups":[124],"that":[125],"might":[126],"independent":[129],"interest.Mathematics":[130],"Subject":[131],"Classifications:":[132],"11P70,":[133],"05B10,":[134],"11R18,":[135],"44A12Keywords:":[136],"Subset":[137],"sums,":[138],"inverse":[139],"problems,":[140],"transform,":[142],"extension":[144]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-10-10T00:00:00"}