On the largest degree of an irreducible factor of a polynomial in F q[X]

Lithuanian Mathematical Journal

Volumn 37, Issue 1, 1997, Pages 38-45

  Knopfmacher, A ^a   Manstavicius E ^b  

^a UNIVERSITY OF THE WITWATERSRAND   (South Africa)

^b VILNIUS UNIVERSITY   (Lithuania)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012770519     PISSN: 03631672     EISSN: 15738825     Source Type: Journal    
DOI: 10.1007/BF02465438     Document Type: Article

References (26)

1. q[X], CR Acad. Sci. Paris, Ser. I, 294, 147-150 (1982).
2. q[X], Acta Arith., 48, 145-165 (1987).
3. P. Erdos and P. Turán, On some problems of a statistical grouptheory I, Z. Wahr. verw. Geb., 4, 175-186 (1965).
4. P. Flajolet and A. Odlyzko, Singularity analysis of generating functions, SIAM J. Discrete Math., 3, 216-240 (1990).
5. P. Flajolet and M. Soria, Gaussian limiting distributions for the number of components in combinatorial structures, J. Combinatorial Theory, Ser. A, 53, 165-182 (1990).
6. V. L. Goncharov, Sur la distribution des cycles dans les permutations, Dokl. Akad. Nauk SSSR, 35, 267-269 (1942).
7. K.-H. Indlekofer and E. Manstavičius, Additive and multiplicative functions on arithmetical semigroups, Publ. Math. Debrecen, 45, 1-17 (1994).
8. A. Knopfmacher, On the number of distinct degree sizes of a polynomial over a finite field (1995) (to appear).
9. A. Knopfmacher and J. Knopfmacher, Counting irreducible factors of polynomials over a finite field, Discrete Math., 112, 103-118 (1993).
10. A. Knopfmacher and J. N. Ridley, Reciprocal sums over partitions and compositions, SIAM J. Discrete Math., 6, 388-399 (1993).
11. A. Knopfmacher and R. Warlimont, Distinct degree factorizations for polynomials over a finite field, Trans. Amer. Math. Soc., 347, 2235-2243 (1995).
12. A. Knopfmacher and R. Warlimont, Counting permutations and polynomials with a restricted factorization pattern (to appear in Australas. J. Combin.).
13. J. Knopfmacher, Direct factors of polynomial rings over finite fields, J. Combin. Theory, Ser. A, 40, 429-434 (1985).
14. V. F. Kolchin and V. P. Chistyakov, On the cycle structure of random permutations, Mat. Zametki, 18, 929-938 (1975).
15. E. Manstavičius, Semigroup elements free of large prime factors, in: New Trends in Probability and Statistics, vol. 2: Analytic and Probabilistic Methods in Number Theory, F. Schweiger and E. Manstavičius (Eds.), TEV, Vilnius/VSP, Utrecht (1992), pp. 135-153.
16. E. Manstavičius, Remarks on the semigroup elements free of large prime factors, Lith. Math. J., 32, 400-410 (1992).
17. E. Manstavičius and R. Skrabutėnas, Summation of the values of multiplicative functions semigroups, Lith. Math. J., 33, 330-340 (1993).
18. E. Manstavičius and R. Skrabutėnas, Local distributions of additive functions on arithmetical semigroups. Preprint 95-11, Vilnius University, Faculty of Mathematics (1995).
19. q[X], Ann. Inst. Henri Poincaré, Sec. B, 19, 113-121 (1983).
20. q[X], Colloq. Math. Soc János Bolyai. Topics in Classical Number Theory, 34, 1127-1162 (1981).
21. J. L. Nicolas, Distribution statistique de l'ordre d'un element du groupe symetrique, Acta Math. Hungar., 45, 96-184 (1985).
22. A. M. Odlyzko, Discrete logarithms in finite fields and their cryptographic significance, Lecture Notes in Computer Science, Advances in Cryptology, 209, 224-314 (1985).
23. L. A. Shepp and S. P. Lloyd, Ordered cycle lengths in a random permutation, Trans. Amer. Math. Soc., 121, 340-357 (1966).
24. R. Warlimont, Arithmetical semigroups, II: sieving by large and small prime elements, sets of multiples, Manuscripta Math., 71, 197-221 (1991).
25. R. Warlimont, Arithmetical semigroups, IV: Selberg's analysis, Arch. Math. (Basel), 60, 58-72 (1993).
26. H. S. Wilf, Three problems in combinatorial asymptotics. J. Combin. Theory. Ser. A, 35, 199-207 (1983).