{"id":"https://openalex.org/W7220926416","doi":"https://doi.org/10.48550/arxiv.2610.09939","title":"Reconstruction of slices of cubes","display_name":"Reconstruction of slices of cubes","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220926416","doi":"https://doi.org/10.48550/arxiv.2610.09939"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09939","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09939","pdf_url":"https://arxiv.org/pdf/2610.09939","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/2610.09939","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072529778","display_name":"Marie-Charlotte Brandenburg","orcid":"https://orcid.org/0000-0002-5721-2325","observed_orcids":["https://orcid.org/0000-0002-5721-2325"]},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Brandenburg, Marie-Charlotte","raw_affiliation_strings":["Marie-Charlotte Brandenburg Ruhr-Universit\u00e4t Bochum"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Marie-Charlotte Brandenburg Ruhr-Universit\u00e4t Bochum","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152564637","display_name":"Juliana Curtis","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Curtis, Juliana","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5119730247","display_name":"Chiara Giardino","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I904495901","display_name":"Ruhr University Bochum","ror":"https://ror.org/04tsk2644","country_code":"DE","type":"education","lineage":["https://openalex.org/I904495901"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Giardino, Chiara","raw_affiliation_strings":["Ruhr-Universit\u00e4t Bochum"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ruhr-Universit\u00e4t Bochum","institution_ids":["https://openalex.org/I904495901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087156374","display_name":"Chiara Meroni","orcid":"https://orcid.org/0000-0002-3992-4345","observed_orcids":["https://orcid.org/0000-0002-3992-4345"]},"institutions":[{"id":"https://openalex.org/I4405257222","display_name":"ETH Institute for Theoretical Studies","ror":"https://ror.org/051d04622","country_code":"CH","type":"facility","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4405257222"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Meroni, Chiara","raw_affiliation_strings":["ETH Institute for Theoretical Studies"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Institute for Theoretical Studies","institution_ids":["https://openalex.org/I4405257222"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157924466","display_name":"Arnau Padrol","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]},{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Padrol, Arnau","raw_affiliation_strings":["Universitat de Barcelona & Centre de Recerca Matem\u00e0tica"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat de Barcelona & Centre de Recerca Matem\u00e0tica","institution_ids":["https://openalex.org/I4210122226","https://openalex.org/I71999127"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9848999977111816,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9848999977111816,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.007000000216066837,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.003100000089034438,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hyperplane-sections","display_name":"hyperplane sections","score":0.734000027179718},{"id":"https://openalex.org/keywords/simple-polytopes","display_name":"simple polytopes","score":0.9120000004768372},{"id":"https://openalex.org/keywords/graph-reconstruction","display_name":"graph reconstruction","score":0.5820000171661377},{"id":"https://openalex.org/keywords/combinatorial-types","display_name":"combinatorial types","score":0.7990000247955322},{"id":"https://openalex.org/keywords/polyhedral-graphs","display_name":"polyhedral graphs","score":0.5920000076293945}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.7878000140190125},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7763000130653381},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.73089998960495},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.7150999903678894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.652999997138977},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6062999963760376},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5443999767303467},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3352999985218048},{"id":"https://openalex.org/C113391598","wikidata":"https://www.wikidata.org/wiki/Q1681391","display_name":"Polytope model","level":3,"score":0.3127000033855438},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.29829999804496765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29750001430511475},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.2865000069141388},{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.2712000012397766},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C78168278","wikidata":"https://www.wikidata.org/wiki/Q5227269","display_name":"Data cube","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09939","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09939","pdf_url":"https://arxiv.org/pdf/2610.09939","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.2610.09939","doi":"https://doi.org/10.48550/arxiv.2610.09939","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09939","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:2610.09939","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09939","pdf_url":"https://arxiv.org/pdf/2610.09939","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/G1791683384","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320323428","funder_display_name":"Universitat de Barcelona"},{"id":"https://openalex.org/G2766336479","display_name":null,"funder_award_id":"541393733","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4532494212","display_name":null,"funder_award_id":"PID2022-137283NB-C21","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G5893294622","display_name":null,"funder_award_id":"SPP 2458","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G84477964","display_name":null,"funder_award_id":"CEX2020-001084-M","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323428","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57"},{"id":"https://openalex.org/F4320327714","display_name":"ETH Z\u00fcrich Foundation","ror":"https://ror.org/03nqkz164"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":"https://ror.org/003x0zc53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220926416.pdf","grobid_xml":"https://content.openalex.org/works/W7220926416.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1563086816","https://openalex.org/W1983278360","https://openalex.org/W1997625405","https://openalex.org/W2063165065","https://openalex.org/W2074536752","https://openalex.org/W2127749196","https://openalex.org/W2593540337","https://openalex.org/W2605255283","https://openalex.org/W2613641366","https://openalex.org/W2773033757","https://openalex.org/W2789828811","https://openalex.org/W4210631977","https://openalex.org/W4231597948","https://openalex.org/W4234956562","https://openalex.org/W4406960284","https://openalex.org/W4417128151"],"related_works":["https://openalex.org/W4417128151","https://openalex.org/W7213394962","https://openalex.org/W7213507269","https://openalex.org/W4400813687","https://openalex.org/W4310921984","https://openalex.org/W190060855","https://openalex.org/W7130717033","https://openalex.org/W6980640500","https://openalex.org/W1860914710","https://openalex.org/W2063165065"],"abstract_inverted_index":{"We":[0,27],"prove":[1],"that":[2,30,47],"the":[3,10,22],"combinatorial":[4],"type":[5],"of":[6,9,24,38],"a":[7,13,32,44],"slice":[8],"cube":[11,25],"by":[12,18,42],"hyperplane":[14],"is":[15],"completely":[16],"determined":[17],"its":[19],"graph,":[20],"within":[21],"class":[23],"slices.":[26],"also":[28],"show":[29],"such":[31],"result":[33],"cannot":[34],"extend":[35],"to":[36],"slices":[37,52],"arbitrary":[39],"simple":[40,45],"polytopes":[41],"constructing":[43],"polytope":[46],"has":[48],"two":[49],"combinatorially":[50],"distinct":[51],"with":[53],"isomorphic":[54],"graphs.":[55]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}