{"id":"https://openalex.org/W4366771268","doi":"https://doi.org/10.37236/10991","title":"On Enumeration and Entropy of Ribbon Tilings","display_name":"On Enumeration and Entropy of Ribbon Tilings","publication_year":2023,"publication_date":"2023-04-21","ids":{"openalex":"https://openalex.org/W4366771268","doi":"https://doi.org/10.37236/10991"},"language":"en","primary_location":{"id":"doi:10.37236/10991","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10991","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p15/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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p15/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086939234","display_name":"Yinsong Chen","orcid":"https://orcid.org/0000-0002-3827-5304"},"institutions":[{"id":"https://openalex.org/I123946342","display_name":"Binghamton University","ror":"https://ror.org/008rmbt77","country_code":"US","type":"education","lineage":["https://openalex.org/I123946342"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yinsong Chen","raw_affiliation_strings":["Binghamton University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Binghamton University","institution_ids":["https://openalex.org/I123946342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048458782","display_name":"Vladislav Kargin","orcid":"https://orcid.org/0000-0002-3408-544X"},"institutions":[{"id":"https://openalex.org/I123946342","display_name":"Binghamton University","ror":"https://ror.org/008rmbt77","country_code":"US","type":"education","lineage":["https://openalex.org/I123946342"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vladislav Kargin","raw_affiliation_strings":["Binghamton University, SUNY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Binghamton University, SUNY","institution_ids":["https://openalex.org/I123946342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I123946342"],"apc_list":null,"apc_paid":null,"fwci":0.1727,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49002849,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"30","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9966999888420105,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9966999888420105,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962000250816345,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tile","display_name":"Tile","score":0.9287097454071045},{"id":"https://openalex.org/keywords/ribbon","display_name":"Ribbon","score":0.7716926336288452},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7053273320198059},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6884444952011108},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6651198267936707},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.640873372554779},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.6183313131332397},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5416233539581299},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5404843091964722},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28814053535461426},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16265106201171875},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15843608975410461},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.05343613028526306}],"concepts":[{"id":"https://openalex.org/C2780728851","wikidata":"https://www.wikidata.org/wiki/Q468402","display_name":"Tile","level":2,"score":0.9287097454071045},{"id":"https://openalex.org/C2780392137","wikidata":"https://www.wikidata.org/wiki/Q17121801","display_name":"Ribbon","level":2,"score":0.7716926336288452},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7053273320198059},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6884444952011108},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6651198267936707},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.640873372554779},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.6183313131332397},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5416233539581299},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5404843091964722},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28814053535461426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16265106201171875},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15843608975410461},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.05343613028526306},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/10991","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10991","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p15/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:2305.06332","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2305.06332","pdf_url":"https://arxiv.org/pdf/2305.06332","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/10991","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10991","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p15/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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4366771268.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1551177513","https://openalex.org/W1653035750","https://openalex.org/W1759836991","https://openalex.org/W1794853190","https://openalex.org/W1942616285","https://openalex.org/W2008263650","https://openalex.org/W2030077996","https://openalex.org/W2065813152","https://openalex.org/W2077206892","https://openalex.org/W2100890748","https://openalex.org/W2110539170","https://openalex.org/W2111313119","https://openalex.org/W2181647213","https://openalex.org/W2763985444","https://openalex.org/W3099126563","https://openalex.org/W4255389307","https://openalex.org/W4322739076"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W2114959296","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W38346124","https://openalex.org/W2502442966","https://openalex.org/W2406961474","https://openalex.org/W2067934601","https://openalex.org/W2138666621","https://openalex.org/W3042106073"],"abstract_inverted_index":{"The":[0],"paper":[1],"considers":[2],"ribbon":[3],"tilings":[4,18,26],"of":[5,14,17,23,27,32,56],"large":[6],"regions":[7,29,83],"and":[8,62,73,84,98],"their":[9],"per-tile":[10,42,91],"entropy":[11,43,61,92],"(the":[12],"logarithm":[13],"the":[15,21,41,54,57,89],"number":[16,22],"divided":[19],"by":[20,30,70,76],"tiles).":[24],"For":[25,48,78],"general":[28],"tiles":[31],"length":[33],"$n$,":[34],"we":[35,52],"give":[36],"an":[37],"upper":[38],"bound":[39],"on":[40],"as":[44,96],"$n":[45],"-":[46,102],"1$.":[47],"growing":[49,79,86],"rectangular":[50],"regions,":[51,88],"prove":[53],"existence":[55],"asymptotic":[58,90],"per":[59],"tile":[60],"show":[63],"that":[64],"it":[65],"is":[66,93],"bounded":[67],"from":[68,74],"below":[69],"$\\log_2":[71],"(n/e)$":[72],"above":[75],"$\\log_2(en)$.":[77],"generalized":[80],"\"Aztec":[81],"Diamond\"":[82],"for":[85],"\"stair\"":[87],"calculated":[94],"exactly":[95],"$1/2$":[97],"$\\log_2(n":[99],"+":[100],"1)":[101],"1$,":[103],"respectively.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
