Enumerating the rationals

Journal of Functional Programming

Volumn 16, Issue 3, 2006, Pages 281-291

  Gibbons, Jeremy ^a   Lester, David ^b   Bird, Richard ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONAL PROGRAMMING;

EID: 33646400853     PISSN: 09567968     EISSN: 14697653     Source Type: Journal    
DOI: 10.1017/S0956796806005880     Document Type: Article

References (13)

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2. Andreev, D. E. On a remarkable enumeration of the positive rational numbers. In Russian. Available at ftp://ftp.mccme.ru/users/vyalyi/matpros/ i2126134.pdf.zip.
3. Bird, R., Gibbons, J. and Jones, G. (1999) Program optimisation, naturally. In: Davies, J., Roscoe, A. W. and Woodcock, J. (eds.), Millenial Perspectives in Computer Science, pp. 13-21. Palgrave.
4. Calkin, N. and Wilf, H. (2000) Recounting the rationals. American Mathematical Monthly, 107(4), 360-363. http://www.math.upenn.edu/~wilf/website/ recounting.pdf.
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6. Dijkstra, E. W. (1982b) EWD 578: More about Function 'fusc'. Selected Writings on Computing: A personal perspective, pp. 230-232. Springer-Verlag.
7. Graham, R. L., Knuth, D. E. and Patashnik, O. (1994) Concrete Mathematics: A foundation for computer science. Second edn. Addison-Wesley.
8. Hinze, R. (2000) Perfect trees and bit-reversal permutations. J. Funct. Program. 10(3), 305-317.
9. Knuth, D. E. (1998) The Art of Computer Programming. Second edn. Vol. 3. Addison-Wesley.
10. Newman, M. (2003) Recounting the rationals, continued. Credited in American Mathematical Monthly. 110, 642-643.
11. Thue, A. (1912) Uber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Skrifter udgivne af Videnskabs-Selskabet i Christiana, 1, 1-67.
12. (Reprinted in Selected Mathematical Papers of Axel Thue, Universitetsforlaget, Oslo, 1977, p413-477.)
13. Yu-Ting, S. (1980) A 'natural' enumeration of non-negative rational numbers. American Mathematical Monthly, 87(1), 25-29.