{"id":"https://openalex.org/W7224013003","doi":"https://doi.org/10.48550/arxiv.2610.33890","title":"The geometric combinatorics of $k$-shuffle polynomials","display_name":"The geometric combinatorics of $k$-shuffle polynomials","publication_year":2026,"publication_date":"2026-10-24","ids":{"openalex":"https://openalex.org/W7224013003","doi":"https://doi.org/10.48550/arxiv.2610.33890"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.33890","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33890","pdf_url":"https://arxiv.org/pdf/2610.33890","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.33890","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159285579","display_name":"Chlo\u00e9 Postel-Vinay","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Postel-Vinay, Chlo\u00e9","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159285579"],"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9990000128746033,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0003000000142492354,"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/T10061","display_name":"Algebraic Geometry and Number Theory","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"}}],"keywords":[{"id":"https://openalex.org/keywords/braid-groups","display_name":"braid groups","score":0.7360000014305115},{"id":"https://openalex.org/keywords/fundamental-group","display_name":"fundamental group","score":0.8130000233650208},{"id":"https://openalex.org/keywords/critical-values","display_name":"critical values","score":0.9259999990463257},{"id":"https://openalex.org/keywords/discriminant-varieties","display_name":"discriminant varieties","score":0.9490000009536743},{"id":"https://openalex.org/keywords/geometric-combinatorics","display_name":"geometric combinatorics","score":0.7279999852180481}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8202000260353088},{"id":"https://openalex.org/C124194741","wikidata":"https://www.wikidata.org/wiki/Q320809","display_name":"Braid","level":2,"score":0.7760999798774719},{"id":"https://openalex.org/C33840335","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid group","level":2,"score":0.6855999827384949},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5659000277519226},{"id":"https://openalex.org/C147441545","wikidata":"https://www.wikidata.org/wiki/Q220409","display_name":"Braid theory","level":3,"score":0.5493999719619751},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.524399995803833},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.49970000982284546},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.43650001287460327},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3732999861240387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3328000009059906},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.2953999936580658},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.2842000126838684},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.26019999384880066}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.33890","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33890","pdf_url":"https://arxiv.org/pdf/2610.33890","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.2610.33890","doi":"https://doi.org/10.48550/arxiv.2610.33890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.33890","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:2610.33890","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.33890","pdf_url":"https://arxiv.org/pdf/2610.33890","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7224013003.pdf","grobid_xml":"https://content.openalex.org/works/W7224013003.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223205936","https://openalex.org/W6980626452","https://openalex.org/W2244259305","https://openalex.org/W2950631808","https://openalex.org/W3105037385","https://openalex.org/W3001503584","https://openalex.org/W2044481107","https://openalex.org/W4403885537","https://openalex.org/W2053636290","https://openalex.org/W2953098529"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"the":[3,29,72,77,92,99,106],"second":[4],"in":[5,40,47,61],"a":[6,14],"series":[7],"of":[8,17,32,50,54,80,88,91],"two":[9],"which":[10,83],"aims":[11],"at":[12],"introducing":[13],"new":[15],"family":[16],"groups":[18,75,79,102,109],"called":[19],"$k$-shuffle":[20,73,100],"braid":[21,74,101,108],"groups,":[22,34],"denoted":[23],"$\\mathcal{B}_{n}(k)$.":[24],"We":[25,69],"focus":[26],"here":[27],"on":[28],"geometrical":[30],"origins":[31],"these":[33],"as":[35],"first":[36],"observed":[37],"by":[38],"Calegari":[39],"arXiv:2105.11265.":[41],"The":[42],"spaces":[43,49],"we":[44,96],"are":[45,48,76],"interested":[46],"complex":[51],"monic":[52],"polynomials":[53],"degree":[55],"$n$":[56],"whose":[57],"critical":[58],"values":[59],"lie":[60],"$\\mathbb{C}":[62],"\\setminus":[63],"\\{1,":[64],"e^{\\frac{2\u03c0i}{k}},":[65],"\\dots,":[66],"e^{\\frac{2\u03c0i":[67],"(k-1)}{k}}\\}$.":[68],"show":[70,97],"that":[71,98],"fundamental":[78],"those":[81],"spaces,":[82],"correspond":[84],"geometrically":[85],"to":[86],"complements":[87],"$k$":[89],"translates":[90],"discriminant":[93],"variety.":[94],"Moreover,":[95],"$\\mathcal{B}_n(k)$":[103],"inject":[104],"into":[105],"larger":[107],"$\\mathcal{B}_{nk}$.":[110]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-28T00:00:00"}
