{"id":"https://openalex.org/W3093742841","doi":"https://doi.org/10.37236/10029","title":"Stability of Stretched Root Systems, Root Posets and Shards","display_name":"Stability of Stretched Root Systems, Root Posets and Shards","publication_year":2021,"publication_date":"2021-08-13","ids":{"openalex":"https://openalex.org/W3093742841","doi":"https://doi.org/10.37236/10029","mag":"3093742841"},"language":"en","primary_location":{"id":"doi:10.37236/10029","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10029","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p38/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p38/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059616526","display_name":"Will Dana","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Will Dana","raw_affiliation_strings":["University of Michigan"],"affiliations":[{"raw_affiliation_string":"University of Michigan","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5059616526"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11057402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9993000030517578,"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/T11567","display_name":"semigroups and automata theory","score":0.995199978351593,"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/root","display_name":"Root (linguistics)","score":0.8246452808380127},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5707241296768188},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5658589601516724},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.563263475894928},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5248054265975952},{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.5051727890968323},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4569244384765625},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4413912892341614},{"id":"https://openalex.org/keywords/root-system","display_name":"Root system","score":0.4410322606563568},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3650432229042053},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2392597794532776},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2322615087032318},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15074554085731506},{"id":"https://openalex.org/keywords/botany","display_name":"Botany","score":0.05835092067718506}],"concepts":[{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.8246452808380127},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5707241296768188},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5658589601516724},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.563263475894928},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5248054265975952},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.5051727890968323},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4569244384765625},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4413912892341614},{"id":"https://openalex.org/C155868670","wikidata":"https://www.wikidata.org/wiki/Q534131","display_name":"Root system","level":2,"score":0.4410322606563568},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3650432229042053},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2392597794532776},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2322615087032318},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15074554085731506},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.05835092067718506},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10029","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10029","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p38/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2010.10582","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.10582","pdf_url":"https://arxiv.org/pdf/2010.10582","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"mag:3093742841","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2010.10582","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2010.10582","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2010.10582","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/10029","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10029","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p38/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1958238899","display_name":"Geometry of Cluster Algebras","funder_award_id":"1855135","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G507497302","display_name":null,"funder_award_id":"1840234","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6103710885","display_name":null,"funder_award_id":"DMS-1840234","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7429376454","display_name":null,"funder_award_id":"DMS-1855135","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3093742841.pdf","grobid_xml":"https://content.openalex.org/works/W3093742841.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W112671161","https://openalex.org/W1765655366","https://openalex.org/W2013529674","https://openalex.org/W2132405036","https://openalex.org/W2138241477","https://openalex.org/W2527906400","https://openalex.org/W2528922794","https://openalex.org/W2620919103","https://openalex.org/W3100438960"],"related_works":["https://openalex.org/W3195661508","https://openalex.org/W2952347511","https://openalex.org/W2282646786","https://openalex.org/W2040891755","https://openalex.org/W2901547970","https://openalex.org/W3101790651","https://openalex.org/W3000443148","https://openalex.org/W3112389788","https://openalex.org/W2091470825","https://openalex.org/W2558082165","https://openalex.org/W2951628108","https://openalex.org/W3208489837","https://openalex.org/W2415139284","https://openalex.org/W2065311049","https://openalex.org/W3096160691","https://openalex.org/W2115305702","https://openalex.org/W2964139606","https://openalex.org/W2949735347","https://openalex.org/W2963667153","https://openalex.org/W2804024573"],"abstract_inverted_index":{"Inspired":[0],"by":[1],"the":[2,23,59,69,72,75,96,99,106],"infinite":[3],"families":[4],"of":[5,25,34,62,81,98,108],"finite":[6],"and":[7,78,92,105],"affine":[8],"root":[9,19,40,76],"systems,":[10],"we":[11,57,67],"define":[12],"a":[13,29,32,39,47,54,89,103],"\"stretching\"":[14],"operation":[15,49],"on":[16,22,50],"general":[17],"crystallographic":[18],"systems":[20],"which,":[21],"level":[24],"Coxeter":[26],"diagrams,":[27],"replaces":[28],"vertex":[30],"with":[31],"path":[33],"unlabeled":[35],"edges.":[36],"We":[37,83],"embed":[38],"system":[41],"into":[42],"its":[43],"stretched":[44,70],"versions":[45],"using":[46],"similar":[48],"individual":[51],"roots.":[52],"For":[53],"fixed":[55],"root,":[56],"describe":[58],"long-term":[60],"behavior":[61],"two":[63],"associated":[64],"structures":[65],"as":[66],"lengthen":[68],"path:":[71],"downset":[73,100],"in":[74],"poset":[77],"Reading's":[79],"arrangement":[80],"shards.":[82],"show":[84],"that":[85],"both":[86],"eventually":[87,102],"admit":[88],"uniform":[90],"description,":[91],"deduce":[93],"enumerative":[94],"consequences:":[95],"size":[97],"is":[101],"polynomial,":[104],"number":[107],"shards":[109],"grows":[110],"exponentially.":[111]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
