{"id":"https://openalex.org/W4416237482","doi":"https://doi.org/10.48550/arxiv.2511.09653","title":"Region level via centralization for hyperplane arrangements and beyond","display_name":"Region level via centralization for hyperplane arrangements and beyond","publication_year":2025,"publication_date":"2025-11-12","ids":{"openalex":"https://openalex.org/W4416237482","doi":"https://doi.org/10.48550/arxiv.2511.09653"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2511.09653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.09653","pdf_url":"https://arxiv.org/pdf/2511.09653","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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/2511.09653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5120302645","display_name":"Finn Southerland","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Southerland, Finn","raw_affiliation_strings":["University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040054297","display_name":"Lani Southern","orcid":"https://orcid.org/0009-0006-5179-8616","observed_orcids":["https://orcid.org/0009-0006-5179-8616"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Southern, Lani","raw_affiliation_strings":["University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":null,"display_name":"Zhou, Su","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhou, Su","raw_affiliation_strings":["University of California , San Diego"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":1.0,"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":1.0,"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":0.0,"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/T10849","display_name":"Finite Group Theory Research","score":0.0,"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/hyperplane-arrangements","display_name":"hyperplane arrangements","score":0.9760000109672546},{"id":"https://openalex.org/keywords/regions-of-hyperplane-arrangements","display_name":"regions of hyperplane arrangements","score":0.8379999995231628},{"id":"https://openalex.org/keywords/centralization","display_name":"centralization","score":0.8270000219345093},{"id":"https://openalex.org/keywords/characteristic-polynomial","display_name":"characteristic polynomial","score":0.9909999966621399},{"id":"https://openalex.org/keywords/exponential-generating-functions","display_name":"exponential generating functions","score":0.7760000228881836},{"id":"https://openalex.org/keywords/bijective-proof","display_name":"bijective proof","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8695999979972839},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7822999954223633},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.6845999956130981},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.629800021648407},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5594000220298767},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5162000060081482},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5056999921798706},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4999000132083893},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4422999918460846},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42910000681877136},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3953999876976013},{"id":"https://openalex.org/C2775956649","wikidata":"https://www.wikidata.org/wiki/Q1189744","display_name":"Pfaffian","level":2,"score":0.3675000071525574},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.3546000123023987},{"id":"https://openalex.org/C132170107","wikidata":"https://www.wikidata.org/wiki/Q834585","display_name":"Semilattice","level":3,"score":0.35120001435279846},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31450000405311584},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.3018999993801117},{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.2924000024795532},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2721000015735626},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.27090001106262207},{"id":"https://openalex.org/C61067352","wikidata":"https://www.wikidata.org/wiki/Q1897429","display_name":"Ultrametric space","level":3,"score":0.25589999556541443},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.09653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.09653","pdf_url":"https://arxiv.org/pdf/2511.09653","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2511.09653","doi":"https://doi.org/10.48550/arxiv.2511.09653","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.09653","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.09653","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2511.09653","pdf_url":"https://arxiv.org/pdf/2511.09653","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416237482.pdf","grobid_xml":"https://content.openalex.org/works/W4416237482.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W221320767","https://openalex.org/W1512087518","https://openalex.org/W2001432829","https://openalex.org/W2138241477","https://openalex.org/W2799246003","https://openalex.org/W4403572718"],"related_works":["https://openalex.org/W103594606","https://openalex.org/W7139968531","https://openalex.org/W3215372021","https://openalex.org/W2027697653","https://openalex.org/W4403572718","https://openalex.org/W7100721101","https://openalex.org/W7163127534","https://openalex.org/W1579784117","https://openalex.org/W6910736394","https://openalex.org/W1997625405"],"abstract_inverted_index":{"In":[0,114,164],"\"Faces":[1],"of":[2,25,27,42,54,60,79,84,111,127,141,147,161,184,192],"a":[3,28,34,55,63,82,119,128],"Hyperplane":[4],"Arrangement":[5],"Enumerated":[6],"by":[7],"Ideal":[8],"Dimension,":[9],"with":[10,33,131],"Applications":[11],"to":[12,20,73,156],"Plane,":[13],"Plaids,":[14],"and":[15,44,66,101,175],"Shi,\"":[16],"Zaslavsky":[17],"showed":[18],"how":[19,168],"compute":[21],"the":[22,58,77,93,107,124,139,179,193],"number":[23],"$r_\\ell(\\mathcal{A})$":[24,89],"regions":[26,43],"real":[29],"hyperplane":[30],"arrangement":[31],"$\\mathcal{A}$":[32],"given":[35],"level,":[36],"refining":[37],"his":[38],"well":[39],"known":[40],"enumeration":[41,86],"relatively":[45],"bounded":[46],"regions.":[47],"We":[48],"restate":[49],"this":[50,85,115],"theorem":[51],"in":[52,70,106,182],"terms":[53,183],"construction":[56],"called":[57],"centralization":[59,102],"$\\mathcal{A}$,":[61],"give":[62],"bijective":[64],"proof,":[65],"then":[67],"apply":[68],"it":[69,152],"two":[71],"ways":[72],"answer":[74],"questions":[75],"concerning":[76],"concept":[78],"level.":[80],"Firstly,":[81],"consequence":[83],"is":[87],"that":[88,98],"depends":[90],"only":[91],"on":[92],"intersection":[94],"poset":[95],"$\\mathcal{L}(\\mathcal{A})$,":[96],"such":[97],"both":[99],"$r_\\ell$":[100,185],"can":[103,153,187],"be":[104,154,188],"defined":[105],"more":[108],"general":[109,121],"setting":[110],"geometric":[112,129],"semilattices.":[113],"context":[116],"we":[117,166],"derive":[118],"very":[120],"expression":[122,177],"for":[123,190],"characteristic":[125,180],"polynomial":[126,181],"semilattice":[130],"several":[132],"interesting":[133],"corollaries.":[134],"Secondly,":[135],"recent":[136],"investigations":[137],"into":[138],"phenomenon":[140],"level":[142],"have":[143],"made":[144],"little":[145],"use":[146],"Zaslavsky's":[148],"level-counting":[149],"theorem,":[150],"but":[151],"applied":[155],"obtain":[157],"or":[158],"generalize":[159],"many":[160],"their":[162],"results.":[163],"particular":[165],"show":[167],"exponential":[169],"generating":[170],"function":[171],"identities":[172],"(arXiv:2410.10198,":[173],"arXiv:2411.02971)":[174],"an":[176],"giving":[178],"(arXiv:2411.03756)":[186],"derived":[189],"deformations":[191],"braid":[194],"arrangement.":[195]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2025-11-15T00:00:00"}
