{"id":"https://openalex.org/W4416942337","doi":"https://doi.org/10.4230/lipics.socg.2026.41","title":"The Depth Poset Under Transpositions in the Filter","display_name":"The Depth Poset Under Transpositions in the Filter","publication_year":2025,"publication_date":"2025-11-26","ids":{"openalex":"https://openalex.org/W4416942337","doi":"https://doi.org/10.4230/lipics.socg.2026.41"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2511.21961","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.21961","pdf_url":"https://arxiv.org/pdf/2511.21961","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,"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.21961","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052977177","display_name":"Herbert Edelsbrunner","orcid":null},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Edelsbrunner, Herbert","raw_affiliation_strings":["Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0002-9823-6833","affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039286285","display_name":"Micha\u0142 Lipi\u0144ski","orcid":"https://orcid.org/0000-0001-9789-9750"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Lipi\u0144ski, Micha\u0142","raw_affiliation_strings":["Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0001-9789-9750","affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072482789","display_name":"Marian Mro\u017cek","orcid":"https://orcid.org/0000-0002-0619-6417"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mrozek, Marian","raw_affiliation_strings":["Division of Computational Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-0619-6417","affiliations":[{"raw_affiliation_string":"Division of Computational Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086730809","display_name":"Manuel Soriano-Trigueros","orcid":"https://orcid.org/0000-0003-2449-1433"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]},{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["AT","ES"],"is_corresponding":false,"raw_author_name":"Soriano-Trigueros, Manuel","raw_affiliation_strings":["Universidad de Sevilla, Spain","Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0000-0003-2449-1433","affiliations":[{"raw_affiliation_string":"Universidad de Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5120580697","display_name":"Fedor Zimin","orcid":null},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Zimin, Fedor","raw_affiliation_strings":["Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria"],"raw_orcid":"https://orcid.org/0009-0009-8877-6682","affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9962000250816345,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9962000250816345,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0005000000237487257,"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/partially-ordered-set","display_name":"Partially ordered set","score":0.9136999845504761},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.6394000053405762},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5040000081062317},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45419999957084656},{"id":"https://openalex.org/keywords/diagram","display_name":"Diagram","score":0.4142000079154968},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.3206000030040741}],"concepts":[{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.9136999845504761},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7943999767303467},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6717000007629395},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.6394000053405762},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5040000081062317},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45419999957084656},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.436599999666214},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.4142000079154968},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38769999146461487},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.3206000030040741},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2897000014781952},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.27129998803138733}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:arXiv.org:2511.21961","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.21961","pdf_url":"https://arxiv.org/pdf/2511.21961","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,"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":"pmh:oai:drops-oai.dagstuhl.de:25847","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.41","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol367-socg2026/LIPIcs.SoCG.2026.41/LIPIcs.SoCG.2026.41.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"pmh:doi:10.4230/lipics.socg.2026.41","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"},{"id":"doi:10.48550/arxiv.2511.21961","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.21961","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,"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.4230/lipics.socg.2026.41","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.socg.2026.41","pdf_url":null,"source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.21961","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.21961","pdf_url":"https://arxiv.org/pdf/2511.21961","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,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"depth":[1,26,58,67],"poset":[2,27,68],"of":[3,14,48,51],"a":[4,44],"filtered":[5],"Lefschetz":[6],"complex":[7],"reflects":[8],"the":[9,12,20,25,29,35,54,57,66,77],"dependencies":[10],"between":[11],"cancellations":[13],"different":[15],"shallow":[16],"birth-death":[17],"pairs.":[18],"Using":[19],"fast":[21],"algorithms":[22],"for":[23,33,69],"computing":[24],"in":[28,53,81],"present":[30,63],"work":[31],"and":[32,73],"updating":[34],"persistence":[36],"diagram":[37],"under":[38],"transpositions":[39,50,78],"(Vineyard":[40],"persistence),":[41],"we":[42,62],"give":[43],"complete":[45],"case":[46],"analysis":[47],"how":[49],"cells":[52],"filter":[55],"affect":[56],"poset.":[59],"In":[60],"addition,":[61],"statistics":[64],"on":[65],"random":[70,82],"point":[71],"data":[72],"its":[74],"sensitivity":[75],"to":[76],"that":[79],"occur":[80],"straight-line":[83],"homotopies.":[84]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-12-03T00:00:00"}