{"id":"https://openalex.org/W2179318252","doi":"https://doi.org/10.1007/s00454-017-9954-z","title":"Zigzag Structure of Thin Chamber Complexes","display_name":"Zigzag Structure of Thin Chamber Complexes","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2179318252","doi":"https://doi.org/10.1007/s00454-017-9954-z","mag":"2179318252"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-017-9954-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9954-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9954-z.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 & Computational Geometry","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9954-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113871341","display_name":"Michel Deza","orcid":null},"institutions":[{"id":"https://openalex.org/I4210162280","display_name":"Laboratoire de G\u00e9ologie de l\u2019\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/05vg9cw43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210148025","https://openalex.org/I4210162280"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Michel Deza","raw_affiliation_strings":["\u00c9cole Normale Sup\u00e9rieure, Paris, France",",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Normale Sup\u00e9rieure, Paris, France","institution_ids":["https://openalex.org/I4210162280"]},{"raw_affiliation_string":",\u00c9cole Normale Sup\u00e9rieure, Paris, France#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060769535","display_name":"Mark Pankov","orcid":"https://orcid.org/0000-0003-2052-0348"},"institutions":[{"id":"https://openalex.org/I47996466","display_name":"University of Warmia and Mazury in Olsztyn","ror":"https://ror.org/05s4feg49","country_code":"PL","type":"education","lineage":["https://openalex.org/I47996466"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Mark Pankov","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, University of\u00a0 Warmia and Mazury, Olsztyn, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, University of\u00a0 Warmia and Mazury, Olsztyn, Poland","institution_ids":["https://openalex.org/I47996466"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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":0.01506024,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":"2","first_page":"363","last_page":"382"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9921000003814697,"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/T11298","display_name":"Synthesis and Properties of Aromatic Compounds","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.8490894436836243},{"id":"https://openalex.org/keywords/zigzag","display_name":"Zigzag","score":0.8053207397460938},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5803790092468262},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5797157287597656},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48845377564430237},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3536219894886017},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.3212299942970276},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30714893341064453},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13586294651031494}],"concepts":[{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.8490894436836243},{"id":"https://openalex.org/C192271897","wikidata":"https://www.wikidata.org/wiki/Q198438","display_name":"Zigzag","level":2,"score":0.8053207397460938},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5803790092468262},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5797157287597656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48845377564430237},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3536219894886017},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.3212299942970276},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30714893341064453},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13586294651031494}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00454-017-9954-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9954-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9954-z.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 & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1509.03754","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1509.03754","pdf_url":"https://arxiv.org/pdf/1509.03754","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":"mag:2179318252","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1509.03754.pdf","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.1509.03754","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1509.03754","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:10.1007/s00454-017-9954-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-017-9954-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-017-9954-z.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 & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2179318252.pdf","grobid_xml":"https://content.openalex.org/works/W2179318252.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W51037165","https://openalex.org/W143000018","https://openalex.org/W153328046","https://openalex.org/W1145633754","https://openalex.org/W1538279012","https://openalex.org/W2009190506","https://openalex.org/W2153142809","https://openalex.org/W2164162886","https://openalex.org/W2204909750","https://openalex.org/W2329714975","https://openalex.org/W2498854486","https://openalex.org/W2955257874","https://openalex.org/W4206570602","https://openalex.org/W4236326697","https://openalex.org/W4298377646"],"related_works":["https://openalex.org/W2963599563","https://openalex.org/W3102226981","https://openalex.org/W2082471587","https://openalex.org/W940944027","https://openalex.org/W1529956391","https://openalex.org/W1986690972","https://openalex.org/W2951639531"],"abstract_inverted_index":{"Zigzags":[0],"in":[1,7,11,28,67,72],"thin":[2,74],"chamber":[3,75],"complexes":[4,14],"are":[5,15,46],"investigated,":[6],"particular,":[8],"all":[9,26],"zigzags":[10,27],"the":[12,23,29,34,39,41,44,49],"Coxeter":[13,50],"described.":[16],"Using":[17],"this":[18],"description,":[19],"we":[20],"show":[21],"that":[22],"lengths":[24],"of":[25,52],"simplex":[30],"$$\\alpha":[31],"_{n}$$":[32,37],",":[33,38,54,56,60,62],"cross-polytope":[35],"$$\\beta":[36],"24-cell,":[40],"icosahedron":[42],"and":[43,58],"600-cell":[45],"equal":[47],"to":[48],"numbers":[51],"$$\\mathsf{A}_{n}$$":[53],"$$\\mathsf{B}_{n}=\\mathsf{C}_{n}$$":[55],"$$\\mathsf{F}_{4}$$":[57],"$$\\mathsf{H}_{i}$$":[59],"$$i=3,4$$":[61],"respectively.":[63],"We":[64],"also":[65],"discuss":[66],"which":[68],"cases":[69],"two":[70],"faces":[71],"a":[73,81],"complex":[76],"can":[77],"be":[78],"connected":[79],"by":[80],"zigzag.":[82]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}