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On sequences of ±1's defined by binary patterns

Seria
Rozprawy Matematyczne tom/nr w serii: 283 wydano: 1989
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
1. Introduction..............................................................5
2. The matrix recursion................................................8
3. The characteristic polynomial of A.........................12
4. The autocorrelation tree........................................15
5. The roots of the period polynomials.......................19
6. A recurrence relation for $s_p(x)$..........................25
7. An explicit formula..................................................30
8. The limit function....................................................34
9. The case P = 111...................................................42
10. The exceptional cases.........................................45
11. The structure of the autocorrelation tree..............51
Appendix....................................................................58
References................................................................59
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 283
Liczba stron
60
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXXXIII
Daty
wydano
1989
Twórcy
  • Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada V6T 1Y4
autor
  • IBM Corporation, Department 17W-BLDG. 630, Route 52, Hopewell Junction, NY 12533 0999, U.S.A.
  • Department of Mathematics, Wellesley College, Wellesley, MA 02181, U.S.A.
Bibliografia
  • [1] J. P. Allouche and J. O. Shallit, Infinite products associated with counting blocks in binary strings, J. London Math. Soc. (to appear).
  • [2] J. Brillhart and L. Carlitz, Note on the Shapiro polynomials, Proc. Amer. Math. Soc. 25 (1970), 114-118.
  • [3] J. Brillhart, On the Rudin-Shapiro polynomials, Duke Math. J. 40 (1973), 335-353.
  • [4] J. Brillhart, J. S. Lomont and P. Morton, Cyclotomic properties of the Rudin-Shapiro polynomials, J. Reine Angew. Math. 288 (1976), 37-65.
  • [5] J. Brillhart and P. Morton, Über Summen von Rudin-Shapiroschen Koeffizienten, Illinois J. Math. 22 (1978), 126-148.
  • [6] J.Brillhart, P. Erdös and P. Morton, On sums of Rudin-Shapiro coefficients, II, Pacific J. Math. 107 (1983), 39-69.
  • [7] G. Christol, T. Kamae, M. Mendes France and G. Rauzy, Suites algebriques, automata et substitutions, Bull. Soc. Math. France 108 (1980), 401-419.
  • [8] J. Coquet, A summation formula related to the binary digits, Invent. Math. 73 (1983), 107-115.
  • [9] M. Dekking, M. Mendes France and A. van der Poorten, Folds!, I, II, III, Math. Intelligencer 4 (1982), 130-138, 173-181, 190-195.
  • [10] H, Delange, Sur la function sommatoire de la fonction "summe des chiffres", Enseign. Math. (2) 21 (1975), 31-47.
  • [11] F. R. Gantmacher, The Theory of Matrices, Vol. II, Chelsea, 1964, p. 53.
  • [12] L. J. Guibas and A. M. Odlyzko, Long repetitive patterns in random sequences, Z. Wahrsch. Verw. Gebiete 53 (1980), 241-262.
  • [13] L. J. Guibas and A. M. Odlyzko, Periods in strings, J. Combin. Theory Ser. A 30 (1981), 19-42.
  • [14] L. J. Guibas and A. M. Odlyzko, String overlaps, pattern matching, and nontransitive games, J. Combin. Theory (A) 30 (1981), 183-208.
  • [15] I. Kaplansky, Fields and Rings, Chicago Lectures in Mathematics, University of Chicago Press, Chicago 1972.
  • [16] A. Ya. Khinchine, Continued Fractions, University of Chicago Press, Chicago 1964.
  • [17] K. Knopp, Infinite Sequences and Series, Dover, 1956.
  • [18] D. H. Lehmer, Mahler's matrices, J. Austral. Math. Soc. 1 (1960), 385 - 395.
  • [19] D. H. and Emma Lehmer, Picturesque exponential sums, I, Amer. Math. Monthly 86 (1979), 725-733.
  • [20] D. H. and Emma Lehmer, Picturesque exponential sums, II, J. Reine Angew. Math. 318 (1980), 1-19.
  • [21] W. J. Leveque, Topics in Number Theory, vol. II, Addison-Wesley Publishing Co., 1956, p. 198.
  • [22] J. E. Littlewood, Some Problems in Real and Complex Analysis, Heath Math. Monographs, D. C. Heath & Co. 1968.
  • [23] K. Mahler, A matrix representation of the primitive residue classes (mod 2n), Proc. Amer. Math. Soc. 8 (1957), 525-531.
  • [24] B. B. Mandelbrot, The Fractal Geometry of Nature. W. H. Freeman and Co., 1983.
  • [25] M. Marden, Geometry of Polynomials, Amer. Math. Soc. Mathematical Surveys no. 3. 1966.
  • [26] M. Mendes France and A. J. van der Porten, Arithmetic and analytic properties of paper folding sequences. Bull. Austral Math. Soc. 24 (1981), 123-131.
  • [27] M. Mendes France, Paper folding, space-filling curves and Rudin-Shapiro sequences, Contemp. Math. 9 (1982), 85-95.
  • [28] M. Mendes France and J. O. Shallit, Some planar curves associated with sums of digits, announcement (preprint).
  • [29] L. M. Milne-Thomson, The Calculus of Finite Differences, Chelsea.
  • [30] I. Niven, Irrational Numbers, Carus Monographs, No, 11, 1956, Ch. 8.
  • [31] D. Rider, Closed subalgebras of L(T), Duke Math. J. 19 (1966), 347-355.
  • [32] W. Rudin, Some theorems on Fourier coefficients, Proc. Amer. Math. Soc. 10 (1959), 855-859.
  • [33] H. S. Shapiro, Extremal problems for polynomials and power series, Master's thesis, M.I.T., 1951.
  • [34] E. C. Titchmarsh, Theory of Functions, Oxford University Press, 1968.
Języki publikacji
EN
Uwagi
1980 Mathematics Subject Classification: Primary 10A30, 10H25
Identyfikator YADDA
bwmeta1.element.zamlynska-00a409cc-b5a9-4e56-988b-aa8b9ed57545
Identyfikatory
ISBN
83-01-09037-5
ISSN
0012-3862
Kolekcja
DML-PL
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