{"id":"https://openalex.org/W7221195682","doi":"https://doi.org/10.48550/arxiv.2610.12036","title":"Constructing pathological symmetric abstract rigidity matroids","display_name":"Constructing pathological symmetric abstract rigidity matroids","publication_year":2026,"publication_date":"2026-10-08","ids":{"openalex":"https://openalex.org/W7221195682","doi":"https://doi.org/10.48550/arxiv.2610.12036"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.12036","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12036","pdf_url":"https://arxiv.org/pdf/2610.12036","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.12036","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001886910","display_name":"Sean Dewar","orcid":"https://orcid.org/0000-0003-2220-4576","observed_orcids":["https://orcid.org/0000-0003-2220-4576"]},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Dewar, Sean","raw_affiliation_strings":["Department of Computer Science , KU Leuven"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , KU Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5092130716","display_name":"Joannes Vermant","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I90267481","display_name":"Ume\u00e5 University","ror":"https://ror.org/05kb8h459","country_code":"SE","type":"education","lineage":["https://openalex.org/I90267481"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Vermant, Joannes","raw_affiliation_strings":["Department of Mathematics and Mathematical Statistics , Ume\u00e5 University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Mathematical Statistics , Ume\u00e5 University","institution_ids":["https://openalex.org/I90267481"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.4050000011920929,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.4050000011920929,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.36079999804496765,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.10859999805688858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.4090000092983246},{"id":"https://openalex.org/keywords/rigidity-theory","display_name":"rigidity theory","score":0.6320000290870667},{"id":"https://openalex.org/keywords/matroid-construction","display_name":"matroid construction","score":0.5849999785423279}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.9337999820709229},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6985999941825867},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6723999977111816},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6621999740600586},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5899999737739563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35260000824928284},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.352400004863739},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.30250000953674316},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30219998955726624},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2321999967098236}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.12036","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12036","pdf_url":"https://arxiv.org/pdf/2610.12036","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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.2610.12036","doi":"https://doi.org/10.48550/arxiv.2610.12036","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.12036","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.12036","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.12036","pdf_url":"https://arxiv.org/pdf/2610.12036","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1005089900","display_name":"Exploiting combinatorial structures for algebraic and geometric decompositions","funder_award_id":"G0F5921N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4869584417","display_name":null,"funder_award_id":"iBOF/23/064","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G4872507874","display_name":null,"funder_award_id":"G023721N","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G562246749","display_name":null,"funder_award_id":"IBOF23/064","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5916652429","display_name":"Matroids in Applied and Combinatorial Commutative Algebra","funder_award_id":"G023721N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G7618753153","display_name":null,"funder_award_id":"G0F5921N","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221195682.pdf","grobid_xml":"https://content.openalex.org/works/W7221195682.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1982700170","https://openalex.org/W1998853144","https://openalex.org/W2013407568","https://openalex.org/W2070613680","https://openalex.org/W2087262103","https://openalex.org/W2093752739","https://openalex.org/W2139834426","https://openalex.org/W3161521274","https://openalex.org/W4232388734","https://openalex.org/W4251345737","https://openalex.org/W4307933731","https://openalex.org/W4393667262","https://openalex.org/W4415936511","https://openalex.org/W7128771025","https://openalex.org/W7164812225"],"related_works":["https://openalex.org/W4299532795","https://openalex.org/W2083160851","https://openalex.org/W2087262103","https://openalex.org/W6929451172","https://openalex.org/W7164812225","https://openalex.org/W7213436375","https://openalex.org/W2987633357","https://openalex.org/W4232388734","https://openalex.org/W2028654888","https://openalex.org/W7167674553"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,16,39],"for":[3],"each":[4],"$d":[5],"\\geq":[6],"2$,":[7],"there":[8],"exist":[9],"infinitely":[10],"many":[11],"symmetric":[12],"abstract":[13,46],"$d$-rigidity":[14,20],"matroids":[15,33],"are":[17,34,41],"not":[18,42],"the":[19,22,26,37],"matroid,":[21,24],"$d$-hyperconnectivity":[23],"or":[25],"$d$-cofactor":[27],"matroid.":[28],"When":[29],"$d=2$,":[30],"our":[31],"constructed":[32],"pathological,":[35],"in":[36],"sense":[38],"they":[40],"contained":[43],"within":[44],"any":[45],"2-rigidity":[47],"matroid":[48],"family.":[49],"Our":[50],"construction":[51],"additionally":[52],"provides":[53],"a":[54,57],"counter-example":[55],"to":[56],"conjecture":[58],"of":[59],"Tyomkyn.":[60]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-10T00:00:00"}