{"id":"https://openalex.org/W2971389668","doi":"https://doi.org/10.37236/9046","title":"A Greedoid and a Matroid Inspired by Bhargava's $p$-Orderings","display_name":"A Greedoid and a Matroid Inspired by Bhargava's $p$-Orderings","publication_year":2021,"publication_date":"2021-07-02","ids":{"openalex":"https://openalex.org/W2971389668","doi":"https://doi.org/10.37236/9046","mag":"2971389668"},"language":"en","primary_location":{"id":"doi:10.37236/9046","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9046","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p6/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p6/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074897310","display_name":"Darij Grinberg","orcid":"https://orcid.org/0000-0002-9661-8432"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Darij Grinberg","raw_affiliation_strings":["University of Minnesota, Twin Cities"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Minnesota, Twin Cities","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081347461","display_name":"Fedor Petrov","orcid":"https://orcid.org/0000-0003-1693-2745"},"institutions":[{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Fedor Petrov","raw_affiliation_strings":["St. Petersburg State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"St. Petersburg State University","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00150763,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11882","display_name":"Plant biochemistry and biosynthesis","score":0.8883000016212463,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T11882","display_name":"Plant biochemistry and biosynthesis","score":0.8883000016212463,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.8241999745368958,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8383932709693909},{"id":"https://openalex.org/keywords/perimeter","display_name":"Perimeter","score":0.8069192171096802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.800705075263977},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.7494625449180603},{"id":"https://openalex.org/keywords/ultrametric-space","display_name":"Ultrametric space","score":0.7315306663513184},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41509008407592773},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.41197535395622253},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15071353316307068},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.0723879337310791}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8383932709693909},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.8069192171096802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.800705075263977},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.7494625449180603},{"id":"https://openalex.org/C61067352","wikidata":"https://www.wikidata.org/wiki/Q1897429","display_name":"Ultrametric space","level":3,"score":0.7315306663513184},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41509008407592773},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41197535395622253},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15071353316307068},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.0723879337310791},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9046","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9046","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p6/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.01965","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.01965","pdf_url":"https://arxiv.org/pdf/1909.01965","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":"mag:2971389668","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1909.01965","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":"doi:10.48550/arxiv.1909.01965","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.01965","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:10.37236/9046","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9046","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p6/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":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":[{"id":"https://openalex.org/F4320328470","display_name":"Mathematisches Forschungsinstitut Oberwolfach","ror":"https://ror.org/001zbj766"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2971389668.pdf","grobid_xml":"https://content.openalex.org/works/W2971389668.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W153959861","https://openalex.org/W629968640","https://openalex.org/W1494748022","https://openalex.org/W1982159488","https://openalex.org/W1997331970","https://openalex.org/W2008423200","https://openalex.org/W2047460558","https://openalex.org/W2267371459","https://openalex.org/W2913358375","https://openalex.org/W4230412582","https://openalex.org/W4231057995"],"related_works":["https://openalex.org/W3181693581","https://openalex.org/W3130429763","https://openalex.org/W1487855796","https://openalex.org/W2964872552","https://openalex.org/W2084619351","https://openalex.org/W1981515128","https://openalex.org/W2015352917","https://openalex.org/W1664849218","https://openalex.org/W2963518458","https://openalex.org/W2291663544","https://openalex.org/W2951041260","https://openalex.org/W2949724087","https://openalex.org/W2127159840","https://openalex.org/W2760698131","https://openalex.org/W3099112887","https://openalex.org/W2964051059","https://openalex.org/W2892882511","https://openalex.org/W2950823330","https://openalex.org/W32160485","https://openalex.org/W2159454743"],"abstract_inverted_index":{"Consider":[0],"a":[1,12,30,59,95,137,152],"finite":[2],"set":[3],"$E$.":[4],"Assume":[5],"that":[6,45,87,129],"each":[7,116],"$e":[8],"\\in":[9,16,27,39],"E$":[10,28],"has":[11],"\"weight\"":[13],"$w":[14],"\\left(e\\right)":[15],"\\mathbb{R}$":[17,40],"assigned":[18,41],"to":[19,42,121,127,164,173],"it,":[20],"and":[21,81,104,125,140,169,188],"any":[22,88,145],"two":[23],"distinct":[24],"$e,":[25],"f":[26],"have":[29],"\"distance\"":[31],"$d":[32],"\\left(e,":[33],"f\\right)":[34],"=":[35],"d":[36],"\\left(f,":[37],"e\\right)":[38],"them,":[43],"such":[44,89],"the":[46,49,70,76,101,113,130,141,149,157,174],"distances":[47],"satisfy":[48],"ultrametric":[50],"triangle":[51],"inequality":[52],"$d(a,b)\\leqslant":[53],"\\max":[54],"\\left\\{d(a,c),d(b,c)\\right\\}$.":[55],"We":[56,85,118,190],"look":[57],"for":[58],"subset":[60,90],"of":[61,63,78,133,144,151,177,196],"$E$":[62],"given":[64,146],"size":[65,147],"with":[66,100],"maximum":[67,178],"perimeter":[68,71,114],"(where":[69],"is":[72,170],"defined":[73],"by":[74,94,110,160,185,214],"summing":[75],"weights":[77],"all":[79,134],"elements":[80,108,218],"their":[82],"pairwise":[83],"distances).":[84],"show":[86,128],"can":[91,219],"be":[92],"found":[93],"greedy":[96],"algorithm":[97],"(which":[98],"starts":[99],"empty":[102],"set,":[103],"then":[105],"adds":[106],"new":[107],"one":[109],"one,":[111],"maximizing":[112],"at":[115],"step).":[117],"use":[119],"this":[120,202],"define":[122,165],"numerical":[123,194],"invariants,":[124],"also":[126,171],"maximum-perimeter":[131,142,210,215],"subsets":[132,143,180,211],"sizes":[135],"form":[136],"strong":[138,175],"greedoid,":[139],"are":[148,212],"bases":[150],"matroid.":[153],"This":[154],"essentially":[155],"generalizes":[156],"\"$P$-orderings\"":[158],"constructed":[159],"Bhargava":[161],"in":[162,181],"order":[163],"his":[166],"generalized":[167],"factorials,":[168],"similar":[172],"greedoid":[176],"diversity":[179],"phylogenetic":[182],"trees":[183],"studied":[184],"Moulton,":[186],"Semple":[187],"Steel.":[189],"further":[191],"discuss":[192],"some":[193],"invariants":[195],"$E,":[197],"w,":[198],"d$":[199],"stemming":[200],"from":[201],"construction,":[203],"as":[204,206],"well":[205],"an":[207],"analogue":[208],"where":[209],"replaced":[213],"tuples":[216],"(i.e.,":[217],"appear":[220],"multiple":[221],"times).":[222]},"counts_by_year":[],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}