{"id":"https://openalex.org/W3166441697","doi":"https://doi.org/10.1145/3406325.3451008","title":"Kronecker products, low-depth circuits, and matrix rigidity","display_name":"Kronecker products, low-depth circuits, and matrix rigidity","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3166441697","doi":"https://doi.org/10.1145/3406325.3451008","mag":"3166441697"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451008","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451008","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","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/A5006981411","display_name":"Josh Alman","orcid":"https://orcid.org/0009-0002-2204-1359"},"institutions":[{"id":"https://openalex.org/I2801851002","display_name":"Harvard University Press","ror":"https://ror.org/006v7bf86","country_code":"US","type":"other","lineage":["https://openalex.org/I136199984","https://openalex.org/I2801851002"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Josh Alman","raw_affiliation_strings":["Harvard University, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Harvard University, USA","institution_ids":["https://openalex.org/I2801851002"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006981411"],"corresponding_institution_ids":["https://openalex.org/I2801851002"],"apc_list":null,"apc_paid":null,"fwci":2.8334,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.91077844,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"772","last_page":"785"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991999864578247,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rigidity","display_name":"Rigidity (electromagnetism)","score":0.8546417951583862},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6814678311347961},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.579012930393219},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5573973655700684},{"id":"https://openalex.org/keywords/kronecker-delta","display_name":"Kronecker delta","score":0.5456356406211853},{"id":"https://openalex.org/keywords/structural-rigidity","display_name":"Structural rigidity","score":0.430976003408432},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40852034091949463},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39669269323349},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2898251414299011},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10599413514137268},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08245828747749329},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07764294743537903},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.0632627010345459}],"concepts":[{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.8546417951583862},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6814678311347961},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.579012930393219},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5573973655700684},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.5456356406211853},{"id":"https://openalex.org/C155759531","wikidata":"https://www.wikidata.org/wiki/Q7625050","display_name":"Structural rigidity","level":2,"score":0.430976003408432},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40852034091949463},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39669269323349},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2898251414299011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10599413514137268},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08245828747749329},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07764294743537903},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0632627010345459},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3406325.3451008","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451008","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1430582609","https://openalex.org/W1530008367","https://openalex.org/W1590864168","https://openalex.org/W1668966671","https://openalex.org/W1972332180","https://openalex.org/W1979175600","https://openalex.org/W1982064072","https://openalex.org/W1996146326","https://openalex.org/W1999072436","https://openalex.org/W2027377011","https://openalex.org/W2033961328","https://openalex.org/W2035532007","https://openalex.org/W2038073775","https://openalex.org/W2061133474","https://openalex.org/W2064790310","https://openalex.org/W2073389244","https://openalex.org/W2120248756","https://openalex.org/W2137442467","https://openalex.org/W2165660804","https://openalex.org/W2553219432","https://openalex.org/W2963271334","https://openalex.org/W2964142086","https://openalex.org/W2971503262","https://openalex.org/W3012796491","https://openalex.org/W3099570205","https://openalex.org/W3116253690","https://openalex.org/W4205717186"],"related_works":["https://openalex.org/W2117531509","https://openalex.org/W4281491244","https://openalex.org/W1501657243","https://openalex.org/W2376925814","https://openalex.org/W3185639949","https://openalex.org/W2347694834","https://openalex.org/W2626846570","https://openalex.org/W3202031437","https://openalex.org/W1976886486","https://openalex.org/W2360897844"],"abstract_inverted_index":{"For":[0],"a":[1,5,44,73],"matrix":[2],"M":[3,14,22],"and":[4],"positive":[6],"integer":[7],"r,":[8],"the":[9,16],"rank":[10,30],"r":[11],"rigidity":[12,40,56,64],"of":[13,19,21,39,46,55,77],"is":[15],"smallest":[17],"number":[18],"entries":[20],"which":[23],"one":[24],"must":[25],"change":[26],"to":[27,43,67],"make":[28],"its":[29],"at":[31],"most":[32],"r.":[33],"There":[34],"are":[35],"many":[36],"known":[37,53],"applications":[38,54],"lower":[41],"bounds":[42,66,71],"variety":[45],"areas":[47],"in":[48,72],"complexity":[49],"theory,":[50],"but":[51],"fewer":[52],"upper":[57,65,70],"bounds.":[58],"In":[59],"this":[60],"paper,":[61],"we":[62],"use":[63],"prove":[68],"new":[69],"few":[74],"different":[75],"models":[76],"computation.":[78],"Our":[79],"results":[80],"include:":[81]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-30T17:31:21.811387","created_date":"2025-10-10T00:00:00"}
