{"id":"https://openalex.org/W1993862070","doi":"https://doi.org/10.1137/0403029","title":"Shrinking Lattice Polyhedra","display_name":"Shrinking Lattice Polyhedra","publication_year":1990,"publication_date":"1990-08-01","ids":{"openalex":"https://openalex.org/W1993862070","doi":"https://doi.org/10.1137/0403029","mag":"1993862070"},"language":"en","primary_location":{"id":"doi:10.1137/0403029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0403029","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084924590","display_name":"J. E. Cremona","orcid":"https://orcid.org/0000-0002-7212-0162"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John Cremona","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086120667","display_name":"Susan Landau","orcid":"https://orcid.org/0000-0003-4826-6134"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Susan Landau","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5192,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6461136,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":"3","first_page":"338","last_page":"348"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9994000196456909,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polyhedron","display_name":"Polyhedron","score":0.8648406267166138},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7565652132034302},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.678132176399231},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"Integer lattice","score":0.5800272822380066},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5692723393440247},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5289984345436096},{"id":"https://openalex.org/keywords/integer-points-in-convex-polyhedra","display_name":"Integer points in convex polyhedra","score":0.495837539434433},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4656893014907837},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24707797169685364},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.22264450788497925},{"id":"https://openalex.org/keywords/half-integer","display_name":"Half-integer","score":0.10668802261352539},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08886763453483582}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.8648406267166138},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7565652132034302},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.678132176399231},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.5800272822380066},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5692723393440247},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5289984345436096},{"id":"https://openalex.org/C147700949","wikidata":"https://www.wikidata.org/wiki/Q6042594","display_name":"Integer points in convex polyhedra","level":4,"score":0.495837539434433},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4656893014907837},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24707797169685364},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.22264450788497925},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.10668802261352539},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08886763453483582},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C123558587","wikidata":"https://www.wikidata.org/wiki/Q4956382","display_name":"Branch and price","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0403029","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0403029","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W2037038460","https://openalex.org/W2045645687","https://openalex.org/W4230547558","https://openalex.org/W4234106236","https://openalex.org/W4244197351","https://openalex.org/W4249564479"],"related_works":["https://openalex.org/W2065803772","https://openalex.org/W3091857200","https://openalex.org/W1536211921","https://openalex.org/W1968875186","https://openalex.org/W2198935113","https://openalex.org/W4298518812","https://openalex.org/W2952161372","https://openalex.org/W2169582012","https://openalex.org/W107540463","https://openalex.org/W1979456269"],"abstract_inverted_index":{"This":[0,126],"paper":[1],"treats":[2],"the":[3,18,39,43,50,66,77,88,93,102,115,121,138,146],"following":[4],"geometric":[5],"problem:":[6],"Given":[7],"vertices":[8],"$x_1":[9],",":[10],"\\cdots":[11],",x_n":[12],"$":[13],"of":[14,68,123,149],"a":[15,30,128],"polyhedron":[16,26],"in":[17,21,38,120,140,166],"integer":[19,51],"lattice":[20],"k":[22],"dimensions,":[23,92],"can":[24],"that":[25,76],"be":[27,61],"\u201cshrunk\u201d":[28],"to":[29,60,86],"similar":[31],"one":[32,34],"(i.e.,":[33],"whose":[35],"sides":[36],"remain":[37],"same":[40],"ratio":[41],"as":[42],"original":[44],"polyhedron)":[45],"while":[46],"still":[47],"remaining":[48],"on":[49,65,144],"lattice?":[52],"A":[53],"necessary":[54],"condition":[55,78],"is":[56,74,79,106,153],"given":[57,85],"for":[58,70,132],"this":[59],"possible,":[62],"which":[63],"depends":[64],"parity":[67],"k;":[69],"$k\\leqq":[71],"4$":[72],"it":[73,152],"shown":[75],"sufficient,":[80],"and":[81,105,113,162],"algorithms":[82,116],"are":[83,159,163],"also":[84],"do":[87],"shrinking.":[89],"In":[90],"two":[91],"algorithm":[94,131,139],"only":[95],"involves":[96],"computing":[97,118],"greatest":[98],"common":[99],"divisors":[100],"over":[101],"Gaussian":[103],"integers":[104],"polynomial":[107,129],"time.":[108],"For":[109],"$k":[110,133],"=":[111,134],"3$":[112],"4":[114],"involve":[117],"g.c.d.s":[119],"algebra":[122],"Hurwitz":[124],"quaternions.":[125],"gives":[127],"time":[130],"4$,":[135],"but":[136],"because":[137],"three":[141],"dimensions":[142],"relies":[143],"determining":[145],"square":[147],"factors":[148],"an":[150],"integer,":[151],"at":[154],"present":[155],"exponential.":[156],"The":[157],"proofs":[158],"remarkably":[160],"simple":[161],"quite":[164],"computational":[165],"nature.":[167]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}