{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T13:45:57Z","timestamp":1751982357846},"reference-count":13,"publisher":"Elsevier BV","issue":"1-3","license":[{"start":{"date-parts":[[1999,2,1]],"date-time":"1999-02-01T00:00:00Z","timestamp":917827200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":5280,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Mathematics"],"published-print":{"date-parts":[[1999,2]]},"DOI":"10.1016\/s0012-365x(98)00174-5","type":"journal-article","created":{"date-parts":[[2002,7,25]],"date-time":"2002-07-25T12:12:16Z","timestamp":1027599136000},"page":"197-206","source":"Crossref","is-referenced-by-count":3,"title":["On the degrees of irreducible factors of polynomials over a finite field"],"prefix":"10.1016","volume":"196","author":[{"given":"Arnold","family":"Knopfmacher","sequence":"first","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0012-365X(98)00174-5_BIB1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0747-7171(08)80011-9","article-title":"Factoring polynomials using fewer random bits","volume":"9","author":"Bach","year":"1990","journal-title":"J. Symbolic Comput."},{"key":"10.1016\/S0012-365X(98)00174-5_BIB2","series-title":"Proc. 22nd Annual Symp. Foundations of Computer Science","first-page":"394","article-title":"Probabilistic algorithms in finite fields","author":"Ben-Or","year":"1981"},{"key":"10.1016\/S0012-365X(98)00174-5_BIB3","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1090\/S0025-5718-1981-0606517-5","article-title":"A new algorithm for factoring polynomials over finite fields","volume":"36","author":"Cantor","year":"1981","journal-title":"Math. Comput."},{"key":"10.1016\/S0012-365X(98)00174-5_BIB4","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1007\/3-540-61440-0_131","article-title":"Random polynomials and polynomial factorization","volume":"vol. 1099","author":"Flajolet","year":"1996","journal-title":"Lecture Notes in Computer Science"},{"key":"10.1016\/S0012-365X(98)00174-5_BIB5","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1137\/0403019","article-title":"Singularity Analysis of generating functions","volume":"3","author":"Flajolet","year":"1990","journal-title":"SIAM J. Discrete Math."},{"key":"10.1016\/S0012-365X(98)00174-5_BIB6","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0097-3165(90)90056-3","article-title":"Gaussian limiting distributions for the number of components in combinatorial structures","volume":"53","author":"Flajolet","year":"1990","journal-title":"J.C.T. Series A"},{"key":"10.1016\/S0012-365X(98)00174-5_BIB7","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/BF01272074","article-title":"Computing Frobenius maps and factoring polynomials","volume":"2","author":"von zur Gathen","year":"1992","journal-title":"Comput. Complexity"},{"key":"10.1016\/S0012-365X(98)00174-5_BIB8","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/0012-365X(93)90227-K","article-title":"Counting irreducible factors of polynomials over a finite field","volume":"112","author":"Knopfmacher","year":"1993","journal-title":"Discrete Math."},{"key":"10.1016\/S0012-365X(98)00174-5_BIB9","doi-asserted-by":"crossref","first-page":"2235","DOI":"10.1090\/S0002-9947-1995-1277121-X","article-title":"Distinct degree factorizations for polynomials over a finite field","volume":"347","author":"Knopfmacher","year":"1995","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.1016\/S0012-365X(98)00174-5_BIB10","volume":"vol. 2","author":"Knuth","year":"1981"},{"key":"10.1016\/S0012-365X(98)00174-5_BIB11","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1016\/0020-0190(90)90195-4","article-title":"On the deterministic complexity of factoring polynomials over finite fields","volume":"33","author":"Shoup","year":"1990","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/S0012-365X(98)00174-5_BIB12","series-title":"Computational and algorithmic problems in finite fields","author":"Shparlinski","year":"1992"},{"key":"10.1016\/S0012-365X(98)00174-5_BIB13","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0097-3165(83)90007-9","article-title":"Three problems in combinatorial asymptotics","volume":"35","author":"Wilf","year":"1983","journal-title":"J.C.T. Ser. A"}],"container-title":["Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X98001745?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0012365X98001745?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T23:24:17Z","timestamp":1556666657000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0012365X98001745"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,2]]},"references-count":13,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[1999,2]]}},"alternative-id":["S0012365X98001745"],"URL":"https:\/\/doi.org\/10.1016\/s0012-365x(98)00174-5","relation":{},"ISSN":["0012-365X"],"issn-type":[{"value":"0012-365X","type":"print"}],"subject":[],"published":{"date-parts":[[1999,2]]}}}