{"id":"https://openalex.org/W2884948322","doi":"https://doi.org/10.1137/17m1125728","title":"On the Number of Distinct Rows of a Matrix with Bounded Subdeterminants","display_name":"On the Number of Distinct Rows of a Matrix with Bounded Subdeterminants","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2884948322","doi":"https://doi.org/10.1137/17m1125728","mag":"2884948322"},"language":"en","primary_location":{"id":"doi:10.1137/17m1125728","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1125728","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006849251","display_name":"Christoph Glanzer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christoph Glanzer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029637448","display_name":"Robert Weismantel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Weismantel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5033406324","display_name":"Rico Zenklusen","orcid":"https://orcid.org/0000-0002-7148-9304"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rico Zenklusen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7924,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.71686358,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"32","issue":"3","first_page":"1706","last_page":"1720"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9988999962806702,"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/T11716","display_name":"Random Matrices and Applications","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/combinatorics","display_name":"Combinatorics","score":0.8016685247421265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7675513625144958},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.5402223467826843},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5321442484855652},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5079651474952698},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4863584637641907},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4649938642978668},{"id":"https://openalex.org/keywords/unimodular-matrix","display_name":"Unimodular matrix","score":0.45009806752204895},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08502450585365295}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8016685247421265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7675513625144958},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.5402223467826843},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5321442484855652},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5079651474952698},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4863584637641907},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4649938642978668},{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.45009806752204895},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08502450585365295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1125728","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1125728","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5072212969","display_name":null,"funder_award_id":"200021-165866","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1971361630","https://openalex.org/W1987985110","https://openalex.org/W1998860119","https://openalex.org/W2005598280","https://openalex.org/W2010583328","https://openalex.org/W2016513380","https://openalex.org/W2020913456","https://openalex.org/W2054459484","https://openalex.org/W2064261226","https://openalex.org/W2064283091","https://openalex.org/W2094610860","https://openalex.org/W2146622645","https://openalex.org/W2320323222","https://openalex.org/W4235786133","https://openalex.org/W4238284510"],"related_works":["https://openalex.org/W2011745869","https://openalex.org/W2088028898","https://openalex.org/W1974942973","https://openalex.org/W2950905816","https://openalex.org/W211627054","https://openalex.org/W1608437562","https://openalex.org/W2083668208","https://openalex.org/W3141916192","https://openalex.org/W2171197936","https://openalex.org/W2103890637"],"abstract_inverted_index":{"Let":[0],"$A":[1],"\\in":[2],"\\mathbb{Z}^{m":[3],"\\times":[4,15],"n}$":[5],"be":[6],"a":[7,18,90,142],"matrix":[8],"with":[9],"$\\mathrm{rank}(A)":[10],"=":[11,80,129],"n$,":[12],"whose":[13],"$(n":[14],"n)$-submatrices":[16],"have":[17],"determinant":[19],"of":[20,48,89,135,137],"at":[21,108],"most":[22,109],"${\\mathop{\\vartriangle}}$":[23],"in":[24,122,144],"absolute":[25],"value.":[26],"Assume":[27],"that":[28,56,103,125],"$A$":[29,138],"does":[30],"not":[31],"contain":[32],"the":[33,46,49,123,132],"zero-row,":[34],"nor":[35],"any":[36],"duplicate":[37],"rows,":[38],"and":[39,70],"neither":[40],"two":[41],"rows":[42,136],"where":[43],"one":[44],"is":[45,85,139],"negation":[47],"other.":[50],"Under":[51],"these":[52],"assumptions,":[53],"we":[54],"show":[55],"$m":[57,71],"\\leq":[58,72],"\\frac{1}{2}":[59,73],"\\cdot":[60,64,74,111],"{\\mathop{\\vartriangle}}^{\\log_2\\log_2{\\mathop{\\vartriangle}}":[61],"+":[62,76,113],"2}":[63],"n^2$":[65],"for":[66,78,127],"${\\mathop{\\vartriangle}}":[67,79,128],"\\geq":[68],"2$":[69],"(n^2":[75,112],"n)$":[77,114],"1$.":[81],"The":[82],"latter":[83],"case":[84],"an":[86],"immediate":[87],"consequence":[88],"well-known":[91],"bound":[92,121],"by":[93,141],"Heller":[94],"[Pacific":[95],"J.":[96],"Math.,":[97],"7":[98],"(1957),":[99],"pp.":[100],"1351--1364]":[101],"showing":[102],"totally":[104],"unimodular":[105],"matrices":[106],"admit":[107],"$\\frac{1}{2}":[110],"distinct":[115],"rows.":[116],"Our":[117],"result":[118],"extends":[119],"Heller's":[120],"sense":[124],"even":[126],"n^{\\mathcal{O}(\\sfrac{1}{\\log\\log":[130],"n})}$,":[131],"number":[133],"$m$":[134],"bounded":[140],"polynomial":[143],"$n$.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
