{"id":"https://openalex.org/W4414425715","doi":"https://doi.org/10.1007/s00454-025-00773-y","title":"Equivariant Tutte Polynomial","display_name":"Equivariant Tutte Polynomial","publication_year":2025,"publication_date":"2025-09-23","ids":{"openalex":"https://openalex.org/W4414425715","doi":"https://doi.org/10.1007/s00454-025-00773-y"},"language":"lv","primary_location":{"id":"doi:10.1007/s00454-025-00773-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00773-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00773-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00773-y.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113063696","display_name":"Mario Bauer","orcid":null},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mario Bauer","raw_affiliation_strings":["Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Konstanz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048999085","display_name":"Mat\u011bj Dole\u017e\u00e1lek","orcid":"https://orcid.org/0000-0002-2128-1601"},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mat\u011bj Dole\u017e\u00e1lek","raw_affiliation_strings":["Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Konstanz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093426985","display_name":"Magdal\u00e9na Mi\u0161inov\u00e1","orcid":null},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Magdal\u00e9na Mi\u0161inov\u00e1","raw_affiliation_strings":["Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Konstanz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik und Statistik, Universit\u00e4t Konstanz, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064803291","display_name":"Semen S\u0142obodianiuk","orcid":"https://orcid.org/0009-0004-0622-3843"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Semen S\u0142obodianiuk","raw_affiliation_strings":["University of Bonn: Rheinische Friedrich-Wilhelms-Universitat Bonn, Bonn, Germany"],"raw_orcid":"https://orcid.org/0009-0004-0622-3843","affiliations":[{"raw_affiliation_string":"University of Bonn: Rheinische Friedrich-Wilhelms-Universitat Bonn, Bonn, Germany","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5093426987","display_name":"Julian Weigert","orcid":"https://orcid.org/0009-0001-3576-8699"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I926574661","display_name":"Leipzig University","ror":"https://ror.org/03s7gtk40","country_code":"DE","type":"education","lineage":["https://openalex.org/I926574661"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Julian Weigert","raw_affiliation_strings":["Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Leipzig, Germany","Universit\u00e4t Leipzig, Leipzig, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften, Leipzig, Germany","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Universit\u00e4t Leipzig, Leipzig, Germany","institution_ids":["https://openalex.org/I926574661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064803291"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.36386215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"76","issue":"1","first_page":"253","last_page":"297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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":0.9998999834060669,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9934999942779541,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9904000163078308,"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/equivariant-map","display_name":"Equivariant map","score":0.8179000020027161},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.8011000156402588},{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.755299985408783},{"id":"https://openalex.org/keywords/equivariant-cohomology","display_name":"Equivariant cohomology","score":0.5871000289916992},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.48089998960494995},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4569000005722046},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.4219000041484833},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4162999987602234}],"concepts":[{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.8179000020027161},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8041999936103821},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8011000156402588},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.755299985408783},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.5871000289916992},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5393000245094299},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.48089998960494995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4797999858856201},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4569000005722046},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.4219000041484833},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C5052557","wikidata":"https://www.wikidata.org/wiki/Q1528306","display_name":"Toric variety","level":2,"score":0.3797000050544739},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33340001106262207},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.3172999918460846},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.31279999017715454},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.2957000136375427},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.2637999951839447},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.26019999384880066},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-025-00773-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00773-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00773-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-025-00773-y","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00773-y","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00773-y.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F8431318309","display_name":"German Academic Exchange Service","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414425715.pdf","grobid_xml":"https://content.openalex.org/works/W4414425715.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W1991672107","https://openalex.org/W2088536807","https://openalex.org/W2309721867","https://openalex.org/W2314768891","https://openalex.org/W2800671993","https://openalex.org/W2963621666","https://openalex.org/W2964127965","https://openalex.org/W3036257878","https://openalex.org/W3137550346","https://openalex.org/W4286859614","https://openalex.org/W4323871302","https://openalex.org/W4387394542","https://openalex.org/W4387464525","https://openalex.org/W4402036918","https://openalex.org/W4405911742"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,71,86],"use":[2],"the":[3,8,18,32,65,79,93],"equivariant":[4,62,90],"cohomology":[5],"ring":[6],"of":[7,20,64,68,78,92,97],"permutohedral":[9],"variety":[10],"to":[11,31],"study":[12],"matroids":[13],"and":[14,29],"their":[15],"invariants.":[16],"Investigating":[17],"pushforward":[19],"matroid":[21,80],"Chern":[22],"classes":[23],"defined":[24],"by":[25,81],"Berget,":[26],"Eur,":[27],"Spink":[28],"Tseng":[30],"product":[33],"space":[34],"$${{\\mathbb":[35],"{P}}}^n":[36],"\\times":[37],"{{\\mathbb":[38],"{P}}}^n$$":[39],"<mml:math":[40],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[41],"<mml:mrow>":[42,44,51],"<mml:msup>":[43,50],"<mml:mi>P</mml:mi>":[45,52],"</mml:mrow>":[46,53,56],"<mml:mi>n</mml:mi>":[47,54],"</mml:msup>":[48,55],"<mml:mo>\u00d7</mml:mo>":[49],"</mml:math>":[57],",":[58],"we":[59],"establish":[60],"an":[61,89],"generalization":[63,91],"Tutte":[66],"polynomial":[67,75,96],"a":[69,98],"matroid.":[70,99],"discuss":[72],"how":[73],"this":[74],"encodes":[76],"properties":[77],"looking":[82],"at":[83],"special":[84],"evaluations.":[85],"further":[87],"introduce":[88],"reduced":[94],"characteristic":[95]},"counts_by_year":[],"updated_date":"2026-06-24T06:17:17.354583","created_date":"2025-10-10T00:00:00"}