On the number of distinct functional graphs of affine-linear transformations over finite fields

Linear Algebra and Its Applications

Volumn 439, Issue 5, 2013, Pages 1312-1320

  Bach, Eric ^a   Bridy, Andrew ^b  

^a University of Wisconsin Madison   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Discrete dynamical systems; Finite fields; Linear algebra

Indexed keywords

CONJUGACY CLASS; DISCRETE DYNAMICAL SYSTEMS; FINITE FIELDS; FUNCTIONAL GRAPHS; NON-ISOMORPHIC; SYMMETRIC GROUPS; TRANSFORMATIONS OVER FINITE FIELDS; UPPER AND LOWER BOUNDS;

DYNAMICAL SYSTEMS; LINEAR ALGEBRA; LINEAR TRANSFORMATIONS;

FINITE ELEMENT METHOD;

EID: 84879238060     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2013.04.014     Document Type: Article

References (23)

1. B. Elspas The theory of autonomous linear sequential networks Linear Sequential Switching Circuits 1965 Holden-Day San Francisco, CA 21 61
2. K.C. Wang Transition graphs of affine transformation on vector spaces over finite fields J. Franklin Inst. 283 1967 55 72
3. D.K. Maslen, and D.N. Rockmore Separation of variables and the computation of Fourier transforms on finite groups I J. Amer. Math. Soc. 10 1997 169 214
4. G.E. Andrews The Theory of Partitions 1998 Cambridge Mathematical Library, Cambridge University Press Cambridge
5. P. Diaconis, J. Fulman, and R. Guralnick On fixed points of permutations J. Algebraic Combin. 28 2008 189 218
6. T. Łuczak, and L. Pyber On random generation of the symmetric group Combin. Probab. Comput. 2 1993 505 512
7. J.D. Dixon Random sets which invariably generate the symmetric group Discr. Math. 105 1992 25 39
8. J. Fulman, and R. Guralnick Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements Trans. Amer. Math. Soc. 364 2012 3023 3070
9. 1 Compos. Math. 98 1995 269 304
10. R. Lidl, and H. Niederreiter Introduction to Finite Fields and their Applications first ed. 1994 Cambridge University Press Cambridge
11. G.H. Hardy, and S. Ramanujan Asymptotic formulæfor the distribution of integers of various types [Proc. London Math. Soc. (2) 16 (1917), 112-132] Collected papers of Srinivasa Ramanujan 2000 AMS Chelsea Publ. Providence, RI 245 261
12. M. Roitman On Zsigmondy primes Proc. Amer. Math. Soc. 125 1997 1913 1919
13. K. Hoffman, and R. Kunze Linear Algebra Second ed. 1971 Prentice-Hall Inc. Englewood Cliffs, N.J.
14. M. Kaminski, and N.H. Bshouty Multiplicative complexity of polynomial multiplication over finite fields J. Assoc. Comput. Mach. 36 1989 150 170
15. E. Bach, and J. Shallit Algorithmic Number Theory Efficient Algorithms Foundations of Computing Series vol. 1 1996 MIT Press Cambridge, MA
16. R.A. Hultquist, G.L. Mullen, and H. Niederreiter Association schemes and derived PBIB designs of prime power order Ars Combin. 25 1988 65 82
17. A.K. Agarwal, and G.L. Mullen Partitions with "(d(a) copies of a" J. Combin. Theory Ser. A 48 1988 120 135
18. D.J.B. Mitchell, Generating functions for various sets of solid partitions, Ph.D. Thesis, Penn. State Univ., 1972
19. V. Arnold Number-theoretical turbulence in Fermat-Euler arithmetics and large Young diagrams geometry statistics J. Math. Fluid Mech. 7 2005 S4 S50
20. P. Kurlberg, C. Pomerance, On a problem of Arnold: the average multiplicative order of a given integer, Algebra Number Theory, in press.
21. F. Luca, and I.E. Shparlinski Average multiplicative orders of elements modulo n Acta Arith. 109 2003 387 411
22. M.R. Murty, M. Rosen, and J.H. Silverman Variations on a theme of Romanoff Int. J. Math. 7 1996 373 391
23. C. Pomerance On primitive divisors of Mersenne numbers Acta Arith. 46 1986 355 367