{"id":"https://openalex.org/W4200431641","doi":"https://doi.org/10.1080/10586458.2021.1994488","title":"On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices","display_name":"On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices","publication_year":2021,"publication_date":"2021-12-13","ids":{"openalex":"https://openalex.org/W4200431641","doi":"https://doi.org/10.1080/10586458.2021.1994488"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2021.1994488","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1994488","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2104.07895","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019670101","display_name":"Alexey Garber","orcid":"https://orcid.org/0000-0002-9474-2077"},"institutions":[{"id":"https://openalex.org/I2802326326","display_name":"The University of Texas Rio Grande Valley","ror":"https://ror.org/02p5xjf12","country_code":"US","type":"education","lineage":["https://openalex.org/I2802326326"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexey Garber","raw_affiliation_strings":["School of Mathematical &amp; Statistical Sciences, University of Texas Rio Grande Valley, Brownsville, TX"],"raw_orcid":"https://orcid.org/0000-0002-9474-2077","affiliations":[{"raw_affiliation_string":"School of Mathematical &amp; Statistical Sciences, University of Texas Rio Grande Valley, Brownsville, TX","institution_ids":["https://openalex.org/I2802326326"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019670101"],"corresponding_institution_ids":["https://openalex.org/I2802326326"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.3409846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"33","issue":"1","first_page":"86","last_page":"99"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/voronoi-diagram","display_name":"Voronoi diagram","score":0.9081225991249084},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8561062812805176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8361996412277222},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8270845413208008},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7865403890609741},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.6145598292350769},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5761854648590088},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5285519361495972},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5215211510658264},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35419201850891113},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18071171641349792},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0697532594203949}],"concepts":[{"id":"https://openalex.org/C24881265","wikidata":"https://www.wikidata.org/wiki/Q757267","display_name":"Voronoi diagram","level":2,"score":0.9081225991249084},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8561062812805176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8361996412277222},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8270845413208008},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7865403890609741},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.6145598292350769},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5761854648590088},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5285519361495972},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5215211510658264},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35419201850891113},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18071171641349792},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0697532594203949},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2021.1994488","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2021.1994488","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.07895","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.07895","pdf_url":"https://arxiv.org/pdf/2104.07895","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":null,"raw_type":"text"},{"id":"pmh:oai:scholarworks.utrgv.edu:mss_fac-1224","is_oa":false,"landing_page_url":"https://scholarworks.utrgv.edu/mss_fac/225","pdf_url":null,"source":{"id":"https://openalex.org/S4306402611","display_name":"ScholarWorks @ UTRGV (The University of Texas Rio Grande Valley)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2802326326","host_organization_name":"The University of Texas Rio Grande Valley","host_organization_lineage":["https://openalex.org/I2802326326"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical and Statistical Sciences Faculty Publications and Presentations","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2104.07895","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.07895","pdf_url":"https://arxiv.org/pdf/2104.07895","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W21857574","https://openalex.org/W610336853","https://openalex.org/W1601038980","https://openalex.org/W1839888400","https://openalex.org/W2012618996","https://openalex.org/W2104314581","https://openalex.org/W2115323880","https://openalex.org/W2131904943","https://openalex.org/W2136531262","https://openalex.org/W2235703521","https://openalex.org/W2276929833","https://openalex.org/W2905041590","https://openalex.org/W2952116694","https://openalex.org/W3102063203","https://openalex.org/W3110742541","https://openalex.org/W4252017042","https://openalex.org/W4254868864","https://openalex.org/W4292408570","https://openalex.org/W4330335516","https://openalex.org/W6638673176"],"related_works":["https://openalex.org/W3104946817","https://openalex.org/W1984669674","https://openalex.org/W4300915973","https://openalex.org/W4287215706","https://openalex.org/W2610298398","https://openalex.org/W4281992692","https://openalex.org/W2145396827","https://openalex.org/W2279239548","https://openalex.org/W4294294347","https://openalex.org/W63976795"],"abstract_inverted_index":{"The":[0,37],"Voronoi":[1,29,38,64,79,109],"conjecture":[2,39,65],"on":[3],"parallelohedra":[4],"claims":[5],"that":[6,12,25,51,62,74],"for":[7,43,55,67],"every":[8,98],"convex":[9],"polytope":[10,30,80],"P":[11,26,60,76,103],"tiles":[13],"Euclidean":[14],"d-dimensional":[15,22],"space":[16],"with":[17],"translations":[18],"there":[19],"exists":[20],"a":[21],"lattice":[23,33],"such":[24],"and":[27],"the":[28,44,56,63,78,84,108],"of":[31,59,81,83],"this":[32,70],"are":[34],"affinely":[35],"equivalent.":[36],"is":[40,49,77],"still":[41],"open":[42],"general":[45],"case":[46],"but":[47],"it":[48],"known":[50],"some":[52],"combinatorial":[53],"restrictions":[54],"face":[57],"structure":[58],"ensure":[61],"holds":[66],"P.":[68],"In":[69],"article,":[71],"we":[72],"prove":[73],"if":[75],"one":[82],"dual":[85],"root":[86],"lattices":[87],"Dd*,":[88],"E6*,":[89],"E7*":[90],"or":[91,93],"E8*=E8":[92],"their":[94],"small":[95],"perturbations,":[96],"then":[97],"parallelohedron":[99],"combinatorially":[100],"equivalent":[101],"to":[102],"in":[104],"strong":[105],"sense":[106],"satisfies":[107],"conjecture.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
