{"id":"https://openalex.org/W4415225379","doi":"https://doi.org/10.1007/s00454-025-00777-8","title":"Self-Affinity of Discs Under Glass-Cut Dissections","display_name":"Self-Affinity of Discs Under Glass-Cut Dissections","publication_year":2025,"publication_date":"2025-10-15","ids":{"openalex":"https://openalex.org/W4415225379","doi":"https://doi.org/10.1007/s00454-025-00777-8"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-025-00777-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00777-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00777-8.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/s00454-025-00777-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054462755","display_name":"Christian Richter","orcid":"https://orcid.org/0000-0001-7055-2490"},"institutions":[{"id":"https://openalex.org/I76198965","display_name":"Friedrich Schiller University Jena","ror":"https://ror.org/05qpz1x62","country_code":"DE","type":"education","lineage":["https://openalex.org/I76198965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian Richter","raw_affiliation_strings":["Institute for Mathematics, Friedrich Schiller University, 07737, Jena, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, Friedrich Schiller University, 07737, Jena, Germany","institution_ids":["https://openalex.org/I76198965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054462755"],"corresponding_institution_ids":["https://openalex.org/I76198965"],"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":0.26418747,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"76","issue":"1","first_page":"466","last_page":"490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12176","display_name":"Optimization and Packing Problems","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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/T11159","display_name":"Manufacturing Process and Optimization","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5873000025749207},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.49779999256134033},{"id":"https://openalex.org/keywords/quadrangle","display_name":"Quadrangle","score":0.4424000084400177},{"id":"https://openalex.org/keywords/dissection","display_name":"Dissection (medical)","score":0.42649999260902405}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5873000025749207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5203999876976013},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45649999380111694},{"id":"https://openalex.org/C27258493","wikidata":"https://www.wikidata.org/wiki/Q7268308","display_name":"Quadrangle","level":2,"score":0.4424000084400177},{"id":"https://openalex.org/C2775862295","wikidata":"https://www.wikidata.org/wiki/Q2660911","display_name":"Dissection (medical)","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.38679999113082886},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3012999892234802},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.22519999742507935},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.22110000252723694}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-025-00777-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00777-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00777-8.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/s00454-025-00777-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-025-00777-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-025-00777-8.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/F4320313941","display_name":"Friedrich-Schiller-Universit\u00e4t Jena","ror":"https://ror.org/05qpz1x62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415225379.pdf","grobid_xml":"https://content.openalex.org/works/W4415225379.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W48700190","https://openalex.org/W1565693814","https://openalex.org/W1967778338","https://openalex.org/W2050300730","https://openalex.org/W2054703096","https://openalex.org/W2061049203","https://openalex.org/W2099303096","https://openalex.org/W2123179125","https://openalex.org/W2797577056"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"A":[1],"topological":[2],"disc":[3,39],"is":[4,20,27,153],"called":[5,21],"n":[6,14,22,59,79,83,89,93,97,117,154],"-self-affine":[7,155],"if":[8,24,129],"it":[9],"has":[10],"a":[11],"dissection":[12,26],"into":[13,40],"affine":[15,132],"images":[16],"of":[17,138],"itself.":[18],"It":[19],"-gc-self-affine":[23,60,80,90,98,118],"the":[25],"obtained":[28],"by":[29],"successive":[30],"glass-cuts,":[31],"which":[32],"are":[33,78,87,96,116],"cuts":[34],"along":[35],"segments":[36],"splitting":[37],"one":[38],"two.":[41],"For":[42],"every":[43,82,100,150],"$$n":[44,102,158],"\\ge":[45,103,159],"2$$":[46],"<mml:math":[47,105,121,161],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[48,106,122,162],"<mml:mrow>":[49,107,123,163],"<mml:mi>n</mml:mi>":[50,108,124,164],"<mml:mo>\u2265</mml:mo>":[51,109,165],"<mml:mn>2</mml:mn>":[52],"</mml:mrow>":[53,111,127,168],"</mml:math>":[54,112,128,169],",":[55,113],"we":[56,147],"characterize":[57],"all":[58,157],"discs.":[61],"All":[62,74],"such":[63],"discs":[64],"turn":[65,140],"out":[66,141],"to":[67,142],"be":[68,143],"either":[69],"triangles":[70,75],"or":[71],"convex":[72,151],"quadrangles.":[73],"and":[76,114],"trapezoids":[77],"for":[81,91,99,119,156],".":[84,94],"Non-trapezoidal":[85],"quadrangles":[86,139],"not":[88],"even":[92],"They":[95],"odd":[101],"7$$":[104],"<mml:mn>7</mml:mn>":[110],"they":[115,130],"$$n=5$$":[120],"<mml:mo>=</mml:mo>":[125],"<mml:mn>5</mml:mn>":[126,166],"aren\u2019t":[131],"kites.":[133],"Only":[134],"four":[135],"one-parameter":[136],"families":[137],"3-gc-self-affine.":[144],"In":[145],"addition,":[146],"show":[148],"that":[149],"quadrangle":[152],"5.$$":[160],"<mml:mo>.</mml:mo>":[167]},"counts_by_year":[],"updated_date":"2026-06-24T06:17:17.354583","created_date":"2025-10-16T00:00:00"}
