{"id":"https://openalex.org/W7225170944","doi":"https://doi.org/10.48550/arxiv.2611.03204","title":"Hammock coordinates for silting subcategories of derived-discrete algebras","display_name":"Hammock coordinates for silting subcategories of derived-discrete algebras","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225170944","doi":"https://doi.org/10.48550/arxiv.2611.03204"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.03204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03204","pdf_url":"https://arxiv.org/pdf/2611.03204","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2611.03204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022759820","display_name":"Shantanu Sardar","orcid":"https://orcid.org/0000-0003-4070-8364","observed_orcids":["https://orcid.org/0000-0003-4070-8364"]},"institutions":[{"id":"https://openalex.org/I88830068","display_name":"Shaanxi Normal University","ror":"https://ror.org/0170z8493","country_code":"CN","type":"education","lineage":["https://openalex.org/I88830068"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sardar, Shantanu","raw_affiliation_strings":["Shaanxi Normal University , China;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shaanxi Normal University , China;","institution_ids":["https://openalex.org/I88830068"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022759820"],"corresponding_institution_ids":["https://openalex.org/I88830068"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9984999895095825,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0003000000142492354,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/bounded-derived-category","display_name":"bounded derived category","score":0.7360000014305115},{"id":"https://openalex.org/keywords/cyclic-group-actions","display_name":"cyclic group actions","score":0.9480000138282776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8561000227928162},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5791000127792358},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5317999720573425},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.47839999198913574},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.46950000524520874},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4016999900341034},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38350000977516174},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.38190001249313354},{"id":"https://openalex.org/C192144188","wikidata":"https://www.wikidata.org/wiki/Q245739","display_name":"Solenoid","level":2,"score":0.3402999937534332},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3059000074863434},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.29490000009536743},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2921999990940094},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C138390121","wikidata":"https://www.wikidata.org/wiki/Q5283219","display_name":"Distributivity","level":3,"score":0.2775000035762787},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.03204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03204","pdf_url":"https://arxiv.org/pdf/2611.03204","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2611.03204","doi":"https://doi.org/10.48550/arxiv.2611.03204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.03204","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2611.03204","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.03204","pdf_url":"https://arxiv.org/pdf/2611.03204","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F4320324137","display_name":"Universidad Nacional de Mar del Plata","ror":"https://ror.org/055eqsb67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225170944.pdf","grobid_xml":"https://content.openalex.org/works/W7225170944.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2912832437","https://openalex.org/W2620434630","https://openalex.org/W4214514073","https://openalex.org/W4361865971","https://openalex.org/W3108544845","https://openalex.org/W2962727514","https://openalex.org/W2949415233","https://openalex.org/W4388140277","https://openalex.org/W4414010300","https://openalex.org/W2751373155"],"abstract_inverted_index":{"We":[0,151],"introduce":[1],"hammock":[2],"coordinates":[3],"to":[4,158,178],"study":[5],"the":[6,14,29,63,71,88,133,141,168,179],"combinatorial":[7],"structure":[8],"of":[9,18,73,79,119,140,164,182],"partial":[10,40,75,116,162,175],"silting":[11,41,76,117,163],"configurations":[12],"in":[13,87,167],"bounded":[15],"derived":[16],"category":[17],"a":[19,35,94,98,137,155,183],"derived-discrete":[20],"algebra":[21],"$\u039b(r,n,m)$.":[22],"By":[23],"extracting":[24],"exact":[25],"integer":[26],"inequalities":[27],"from":[28],"Bobi\u0144ski--Gei\u00df--Skowro\u0144ski":[30],"Hom-hammock":[31],"formula,":[32],"we":[33,55,61,103,130],"establish":[34,56],"closed-form":[36],"criterion":[37],"for":[38,122],"pairwise":[39,161],"both":[42],"within":[43,93],"any":[44,74],"$\\mathcal":[45,80],"Z$-component":[46],"and":[47,91],"across":[48],"distinct":[49],"components.":[50],"Using":[51],"this":[52,106],"coordinate":[53,184],"framework,":[54],"three":[57],"primary":[58],"results.":[59],"First,":[60],"prove":[62,104],"universal":[64],"upper":[65],"bound":[66,107],"$|S|":[67],"\\le":[68],"n+m$":[69],"on":[70],"cardinality":[72],"configuration":[77,118,134],"$S$":[78],"Z$-objects":[81],"---both":[82],"globally":[83],"via":[84,97],"Bongartz":[85],"completion":[86],"silting-discrete":[89],"setting,":[90],"combinatorially":[92],"single":[95],"component":[96],"$\u03a3^r$-invariant":[99],"staircase":[100],"argument.":[101],"Second,":[102],"that":[105,132],"is":[108],"universally":[109],"sharp":[110],"by":[111,153],"constructing":[112],"an":[113],"explicit":[114],"L-shaped":[115],"size":[120],"$n+m$":[121],"every":[123],"$\u039b(r,n,m)$,":[124],"alongside":[125],"specialized":[126],"diagonal":[127],"configurations.":[128],"Third,":[129],"show":[131],"lattice":[135,169],"carries":[136],"faithful":[138],"action":[139],"cyclic":[142],"group":[143],"$\\mathbb":[144],"Z/g$":[145],"where":[146],"$g":[147],"=":[148],"\\gcd(r+m,":[149],"n-r)$.":[150],"conclude":[152],"showing":[154],"structural":[156],"obstruction":[157],"local":[159],"determination:":[160],"consecutive":[165],"objects":[166],"ordering":[170],"does":[171],"not":[172],"imply":[173],"global":[174],"silting,":[176],"due":[177],"strict":[180],"additivity":[181],"defect":[185],"along":[186],"chains.":[187]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-11-04T00:00:00"}
