{"id":"https://openalex.org/W7214890715","doi":"https://doi.org/10.48550/arxiv.2609.37867","title":"Absolute moved spaces and noncrossing partition posets in arbitrary Coxeter groups","display_name":"Absolute moved spaces and noncrossing partition posets in arbitrary Coxeter groups","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214890715","doi":"https://doi.org/10.48550/arxiv.2609.37867"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37867","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37867","pdf_url":"https://arxiv.org/pdf/2609.37867","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/2609.37867","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055845079","display_name":"Thomas Gobet","orcid":"https://orcid.org/0000-0003-0103-7430","observed_orcids":["https://orcid.org/0000-0003-0103-7430"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gobet, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5055845079"],"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":0.9990000128746033,"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":0.9990000128746033,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":9.999999747378752e-05,"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/coxeter-groups","display_name":"Coxeter groups","score":0.9950000047683716},{"id":"https://openalex.org/keywords/coxeter-element","display_name":"Coxeter element","score":0.9810000061988831},{"id":"https://openalex.org/keywords/reflection-subgroups","display_name":"reflection subgroups","score":0.8109999895095825},{"id":"https://openalex.org/keywords/lattices","display_name":"lattices","score":0.8619999885559082},{"id":"https://openalex.org/keywords/geometric-representation","display_name":"geometric representation","score":0.7289999723434448}],"concepts":[{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.9240000247955322},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7904999852180481},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6820999979972839},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6733999848365784},{"id":"https://openalex.org/C140860697","wikidata":"https://www.wikidata.org/wiki/Q5179941","display_name":"Coxeter element","level":3,"score":0.6011999845504761},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.58160001039505},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.503000020980835},{"id":"https://openalex.org/C48495023","wikidata":"https://www.wikidata.org/wiki/Q6673739","display_name":"Longest element of a Coxeter group","level":5,"score":0.47870001196861267},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C57796230","wikidata":"https://www.wikidata.org/wiki/Q899720","display_name":"Point group","level":2,"score":0.43220001459121704},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.42809998989105225},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C2781458696","wikidata":"https://www.wikidata.org/wiki/Q7307244","display_name":"Reflection group","level":4,"score":0.3531999886035919},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C37486056","wikidata":"https://www.wikidata.org/wiki/Q5179939","display_name":"Coxeter complex","level":4,"score":0.3249000012874603},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3208000063896179},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.3142000138759613},{"id":"https://openalex.org/C201064014","wikidata":"https://www.wikidata.org/wiki/Q3956993","display_name":"Artin group","level":3,"score":0.29820001125335693},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28999999165534973},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2858000099658966},{"id":"https://openalex.org/C114645060","wikidata":"https://www.wikidata.org/wiki/Q5431294","display_name":"Faithful representation","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C140002607","wikidata":"https://www.wikidata.org/wiki/Q901446","display_name":"Hasse diagram","level":3,"score":0.26840001344680786},{"id":"https://openalex.org/C196773441","wikidata":"https://www.wikidata.org/wiki/Q1475294","display_name":"Maximal element","level":3,"score":0.26269999146461487},{"id":"https://openalex.org/C40233952","wikidata":"https://www.wikidata.org/wiki/Q768074","display_name":"Weyl group","level":2,"score":0.2540000081062317}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37867","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37867","pdf_url":"https://arxiv.org/pdf/2609.37867","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.2609.37867","doi":"https://doi.org/10.48550/arxiv.2609.37867","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37867","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:2609.37867","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37867","pdf_url":"https://arxiv.org/pdf/2609.37867","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/G3499056274","display_name":"Categories, Geometry, Braids","funder_award_id":"ANR-25-CE40-4162","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214890715.pdf","grobid_xml":"https://content.openalex.org/works/W7214890715.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4386345927","https://openalex.org/W4415462644","https://openalex.org/W2766688782","https://openalex.org/W7098035598","https://openalex.org/W4408445354","https://openalex.org/W2953761297","https://openalex.org/W2003047684","https://openalex.org/W7099674619","https://openalex.org/W2060940249","https://openalex.org/W2950787097"],"abstract_inverted_index":{"The":[0],"interval":[1],"$[1,c]_T$":[2,87,205,245,271],"between":[3],"the":[4,13,25,34,65,76,89,101,109,129,138,201,216,226,241],"identity":[5],"element":[6,10,55,114,143],"and":[7,47,82,124,167,173,197,251,264],"a":[8,17,22,45,84,135,237,275],"Coxeter":[9,18,149,259,267],"$c$":[11],"in":[12,64,100,122,146,194,225],"absolute":[14,178,227],"order":[15],"on":[16],"group":[19],"$W$":[20,32,38,106,247],"is":[21,33,39,43,49,96,107,229],"generalization":[23],"of":[24,27,69,80,86,91,93,103,112,141,157,162,188,209,240,244,257,261,266],"poset":[26,42],"noncrossing":[28,189],"partitions":[29],"arising":[30],"when":[31,246],"symmetric":[35],"group.":[36],"When":[37,105],"finite,":[40],"this":[41],"always":[44,164,230],"lattice,":[46],"it":[48],"natural":[50,202],"to":[51,53,75,171,184,198,206,212,273],"associate":[52],"every":[54],"$w\\in":[56,115,144,213],"[1,c]_T$":[57,116,145,214],"its":[58],"\\textit{moved":[59],"space}":[60,156],"$\\mathsf{Mov}(w)=\\mathrm{Im}(w":[61],"-":[62],"\\mathrm{Id}_V)$":[63],"geometric":[66],"representation":[67],"$V$":[68,163],"$W$.":[70],"It":[71,95],"has":[72,119,168,248],"dimension":[73,120,169],"equal":[74,170],"reflection":[77,207],"length":[78],"$\\ell_T(w)$":[79,121],"$w$,":[81],"gives":[83],"realization":[85],"inside":[88],"lattice":[90,242],"subspaces":[92],"$V$.":[94],"an":[97,113,142,147],"important":[98],"tool":[99],"study":[102],"$[1,c]_T$.":[104],"infinite,":[108],"moved":[110,131,139,155,179],"space":[111,140],"no":[117],"longer":[118],"general,":[123],"distinct":[125,174,177],"elements":[126,175,268],"may":[127],"have":[128,176],"same":[130],"space.":[132],"We":[133],"propose":[134],"replacement":[136],"for":[137,269],"arbitrary":[148],"group,":[150],"that":[151,192,200],"we":[152,234],"call":[153],"\\textit{absolute":[154],"$w$.":[158],"This":[159,181],"subspace":[160],"$\\mathsf{AM}(w)$":[161],"contains":[165],"$\\mathsf{Mov}(w)$":[166],"$\\ell_T(w)$,":[172],"spaces.":[180],"allows":[182],"us":[183],"derive":[185,236],"several":[186],"properties":[187],"partition":[190],"posets":[191],"hold":[193],"full":[195],"generality,":[196],"show":[199],"map":[203],"from":[204],"subgroups":[208],"$W$,":[210],"which":[211,270],"associates":[215],"subgroup":[217],"$P(w)$":[218],"generated":[219],"by":[220],"reflections":[221],"lying":[222],"below":[223],"$w$":[224],"order,":[228],"injective.":[231],"Among":[232],"others,":[233],"also":[235],"new":[238,255],"proof":[239],"property":[243],"rank":[249,262],"three,":[250],"exhibit":[252],"infinitely":[253],"many":[254],"examples":[256],"infinite":[258],"groups":[260],"four":[263],"choices":[265],"fails":[272],"be":[274],"lattice.":[276]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-01T00:00:00"}