{"id":"https://openalex.org/W2003418895","doi":"https://doi.org/10.1016/j.dam.2005.02.006","title":"k-th order symmetric SAC boolean functions and bisecting binomial coefficients","display_name":"k-th order symmetric SAC boolean functions and bisecting binomial coefficients","publication_year":2005,"publication_date":"2005-05-05","ids":{"openalex":"https://openalex.org/W2003418895","doi":"https://doi.org/10.1016/j.dam.2005.02.006","mag":"2003418895"},"language":"en","primary_location":{"id":"doi:10.1016/j.dam.2005.02.006","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.dam.2005.02.006","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied 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/A5010080149","display_name":"Thomas W. Cusick","orcid":"https://orcid.org/0000-0002-0087-8855"},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T.W. Cusick","raw_affiliation_strings":["Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076480463","display_name":"Yuan Li","orcid":"https://orcid.org/0000-0002-7637-598X"},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuan Li","raw_affiliation_strings":["Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA","institution_ids":["https://openalex.org/I63190737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I63190737"],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":null,"fwci":2.7592,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.90820225,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"149","issue":"1-3","first_page":"73","last_page":"86"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9965000152587891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9222840070724487},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.766264796257019},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.677237868309021},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6002563238143921},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5992817878723145},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5902289748191833},{"id":"https://openalex.org/keywords/gaussian-binomial-coefficient","display_name":"Gaussian binomial coefficient","score":0.5521907210350037},{"id":"https://openalex.org/keywords/central-binomial-coefficient","display_name":"Central binomial coefficient","score":0.4536168575286865},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40665096044540405},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.2651369571685791},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.17254868149757385},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.05034160614013672}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9222840070724487},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.766264796257019},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.677237868309021},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6002563238143921},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5992817878723145},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5902289748191833},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.5521907210350037},{"id":"https://openalex.org/C134087691","wikidata":"https://www.wikidata.org/wiki/Q1045966","display_name":"Central binomial coefficient","level":4,"score":0.4536168575286865},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40665096044540405},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.2651369571685791},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17254868149757385},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.05034160614013672},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.dam.2005.02.006","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.dam.2005.02.006","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied 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":11,"referenced_works":["https://openalex.org/W1591542597","https://openalex.org/W1670558497","https://openalex.org/W2026118194","https://openalex.org/W2038488511","https://openalex.org/W2076402408","https://openalex.org/W2143814666","https://openalex.org/W2151933547","https://openalex.org/W2168771278","https://openalex.org/W2231898687","https://openalex.org/W6630175629","https://openalex.org/W6631188861"],"related_works":["https://openalex.org/W4225635267","https://openalex.org/W3214798365","https://openalex.org/W2047523883","https://openalex.org/W4212980217","https://openalex.org/W3127361608","https://openalex.org/W4282583869","https://openalex.org/W2266792609","https://openalex.org/W2962898873","https://openalex.org/W2780957143","https://openalex.org/W2086384791"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
