{"id":"https://openalex.org/W7170695099","doi":"https://doi.org/10.48550/arxiv.2607.20717","title":"Shellability of relative squeezed balls and spheres","display_name":"Shellability of relative squeezed balls and spheres","publication_year":2026,"publication_date":"2026-07-22","ids":{"openalex":"https://openalex.org/W7170695099","doi":"https://doi.org/10.48550/arxiv.2607.20717"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2607.20717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.20717","pdf_url":"https://arxiv.org/pdf/2607.20717","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/2607.20717","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5143600234","display_name":"Luz Elena Grisales G\u00f3mez","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":true,"raw_author_name":"G\u00f3mez, Luz Elena Grisales","raw_affiliation_strings":["Department of Mathematics University of Washington Seattle , WA 98195-4350 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Washington Seattle , WA 98195-4350 , USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5143600234"],"corresponding_institution_ids":["https://openalex.org/I201448701"],"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":0.986299991607666,"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":0.986299991607666,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.008999999612569809,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.0006000000284984708,"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/shellability","display_name":"shellability","score":0.890999972820282},{"id":"https://openalex.org/keywords/cyclic-polytopes","display_name":"cyclic polytopes","score":0.7979999780654907},{"id":"https://openalex.org/keywords/simplicial-spheres","display_name":"simplicial spheres","score":0.8320000171661377},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.7689999938011169}],"concepts":[{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6539999842643738},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.5371999740600586},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5349000096321106},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5049999952316284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.490200012922287},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4352000057697296},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37279999256134033},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.28949999809265137},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26429998874664307},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26339998841285706},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.26100000739097595}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2607.20717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.20717","pdf_url":"https://arxiv.org/pdf/2607.20717","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.2607.20717","doi":"https://doi.org/10.48550/arxiv.2607.20717","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.20717","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:2607.20717","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2607.20717","pdf_url":"https://arxiv.org/pdf/2607.20717","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/G3622234865","display_name":"Combinatorics, Algebra, and Geometry of Simplicial Complexes","funder_award_id":"2246399","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7170695099.pdf","grobid_xml":"https://content.openalex.org/works/W7170695099.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4390783985"],"related_works":["https://openalex.org/W2903132558","https://openalex.org/W2068501280","https://openalex.org/W7097887662","https://openalex.org/W2952513339","https://openalex.org/W1978322867","https://openalex.org/W2020109440","https://openalex.org/W4366229276","https://openalex.org/W2094109393","https://openalex.org/W2980637232","https://openalex.org/W1984174158"],"abstract_inverted_index":{"Squeezed":[0],"balls":[1,76],"and":[2,26,38,77,88],"spheres,":[3],"introduced":[4,28],"by":[5,70],"Kalai,":[6],"form":[7],"a":[8],"rich":[9],"class":[10,100],"of":[11,17,35,45,101],"triangulated":[12],"complexes":[13,52,80],"arising":[14],"from":[15],"subcomplexes":[16],"cyclic":[18],"polytopes,":[19],"with":[20],"well-understood":[21],"shellability":[22,59],"properties.":[23],"Recently,":[24],"Novik":[25],"Zheng":[27],"relative":[29,74],"squeezed":[30,36,75],"balls,":[31,37],"obtained":[32],"as":[33],"differences":[34],"used":[39],"them":[40],"to":[41,55],"construct":[42],"large":[43],"families":[44],"highly":[46],"neighborly":[47],"simplicial":[48],"spheres.":[49],"While":[50],"these":[51],"are":[53,81],"known":[54],"be":[56],"constructible,":[57],"their":[58,78],"has":[60],"remained":[61],"open.":[62],"In":[63],"this":[64,68,98],"paper,":[65],"we":[66],"resolve":[67],"question":[69],"proving":[71],"that":[72],"both":[73],"boundary":[79],"shellable.":[82],"We":[83],"provide":[84],"explicit":[85],"shelling":[86],"orders":[87],"characterize":[89],"restriction":[90],"faces,":[91],"thereby":[92],"establishing":[93],"strong":[94],"combinatorial":[95],"structure":[96],"for":[97],"new":[99],"complexes.":[102]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-07-25T00:00:00"}
