Clemens Heuberger — Publications

Please note: All items are copyrighted either by the author or the publisher!

Appeared

  1. On a Family of Quintic Thue Equations, J. Symbolic Comput. 26 (1998), 173–185.
  2. Complete solution of parametrized Thue equations, joint work with A. Pethö and R. F. Tichy, Acta Mathematica et Informatica Universitatis Ostraviensis 6 (1998), 93–113.
  3. On Families of parametrized Thue Equations, Journal of Number Theory 76 (1999), 45–61.
  4. Effective solution of families of Thue Equations containing several parameters, joint work with R. F. Tichy, Acta Arithmetica 91 (1999), 147–163.
  5. On the generalized Ramanujan-Nagell equation x^2+D=p^z, joint work with M.-H. Le, Journal of Number Theory 78 (1999), 312–331.
  6. On general families of parametrized Thue equations, Algebraic Number Theory and Diophantine Analysis, Proceedings of the International Conference held in Graz, August 30 to September 5, 1998 (F. Halter-Koch and R. F. Tichy, eds.), Walter de Gruyter, 2000, pp. 215–238.
  7. Minimal expansions in redundant number systems and shortest paths in graphs, Computing 63 (1999), 341–349.
  8. On a conjecture of E. Thomas concerning parametrized Thue equations, Acta Arithmetica 98 (2001), 375–394. (pdf)
  9. On Minimal Expansions in Redundant Number Systems: Algorithms and Quantitative Analysis, joint work with H. Prodinger, Computing 66 (2001), 377–393. (pdf).
  10. On Explicit Bounds for the Solutions of a Class of Parametrized Thue Equations of Arbitrary Degree, Monatsh. Math. 132 (2001), 325–339. (pdf)
  11. On Hamiltonian Toeplitz Graphs, Discrete Math. 245 (2002), 107–125; earlier version available as SFB Report 182.
  12. Thomas' family of Thue equations over imaginary quadratic fields, joint work with A. Pethö and R. F. Tichy, J. Symbolic Comput. 34 (2002), 437–449. (pdf)
  13. Minimal Redundant Digit Expansions in the Gaussian Integers, J. Théor. Nombres Bordeaux. 14 (2002), 517–528. (pdf) A Mathematica package is available.
  14. Carry Propagation in Signed Digit Representations, joint work with H. Prodinger, European J. Combin. 24 (2003), 293–320. (pdf)
  15. On Planarity and Colorability of Circulant Graphs, Discrete Math. 68 (2003), 153–169. (pdf); earlier version available as SFB Report 197.
  16. Subblock occurrences in signed digit representations, joint work with P. Grabner and H. Prodinger, Glasg. Math. J. 45 (2003), 427–440. (pdf)
  17. Distribution Results for Low-Weight Binary Representations for Pairs of Integers, joint work with P. Grabner and H. Prodinger, Theoret. Comput. Sci. 319 (2004), 307–331. (pdf)
  18. Automatic Solution of Families of Thue equations and an Example of Degree 8, joint work with A. Togbé and V. Ziegler, J. Symbolic Comput. 38 (2004), 1145–1163. (pdf)
  19. Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results, J. Comb. Optim. 8 (2004), 329–361. (pdf); earlier version available as SFB Report 219.
  20. Minimal Expansions in Redundant Number Systems: Fibonacci Bases and Greedy Algorithms, Period. Math. Hungar. 49 (2004), 65–89. (pdf)
  21. Counting Optimal Joint Digit Expansions, joint work with P. Grabner and H. Prodinger, Integers 5 (3) (2005), A9, available at http://www.integers-ejcnt.org/.
  22. The Alternating Greedy Expansion and Applications to Left-To-Right Algorithms in Cryptography, joint work with R. Katti, H. Prodinger, and X. Ruan, Theoret. Comput. Sci 341 (2005), 55–72. (pdf)
  23. Analysis of linear combination algorithms in cryptography, joint work with P. Grabner, H. Prodinger and J. Thuswaldner, ACM Trans. Algorithms 1 (2005), 123–142. (pdf) Online resources.
  24. Analysis of Alternative Digit Sets for Nonadjacent Representations, joint work with H. Prodinger, Monatsh. Math. 147 (2006), 219–248. (pdf)
  25. Minimality of the Hamming Weight of the τ-NAF for Koblitz Curves and Improved Combination with Point Halving, joint work with R. Avanzi and H. Prodinger, Selected Areas in Cryptography: 12th International Workshop, SAC 2005, Kingston, ON, Canada, August 11–12, 2005, Revised Selected Papers (B. Preneel and St. Tavares, eds.), Lecture Notes in Comput. Sci.3897 (2006), 332–344. (pdf)
  26. On the number of optimal base 2 representations of integers, joint work with P. Grabner, Des. Codes Cryptogr. 40 (2006), 25–39. (pdf)
  27. All Solutions to Thomas' Family of Thue Equations over Imaginary Quadratic Number Fields, J. Symbolic Comput. 41 (2006), 980–998. (pdf)
  28. Scalar Multiplication on Koblitz Curves Using the Frobenius Endomorphism and its Combination with Point Halving: Extensions and Mathematical Analysis, joint work with R. Avanzi and H. Prodinger, Algorithmica 46 (2006), 249–270. (pdf)
  29. Parametrized Thue Equations — A survey, Proceedings of the RIMS symposium “Analytic Number Theory and Surrounding Areas”, Kyoto, Oct 18–22, 2004, RIMS Kôkyûroku 1511, August 2006, 82–91. (pdf)
  30. On α-greedy expansions of numbers, joint work with H. Prodinger, Adv. in Appl. Math. 38 (2007), 505–525. (pdf).
  31. Thomas' family of Thue equations over imaginary quadratic fields. II, joint work with A. Pethö and R. F. Tichy, Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 142 (2006), 3–7. (pdf).
  32. The Hamming Weight of the Non-Adjacent-Form under Various Input Statistics, joint work with H. Prodinger, Period. Math. Hungar. 55 (2007), 81–96. (Earlier version available as report 2007-1.)
  33. On Redundant τ-adic Expansions and Non-Adjacent Digit Sets, joint work with R. Avanzi and H. Prodinger, Selected Areas in Cryptography: 13th International Workshop, SAC 2006, Montreal, Canada, August 2006, Revised Selected Papers (E. Biham and A. M. Youssef, eds), Lecture Notes in Comput. Sci. 4356 (2007), 285--301. (Earlier version available as report 2006-14.)
  34. Hwang's Quasi-Power-Theorem in Dimension Two, Quaest. Math. 30 (2007), 507--512. (Earlier version available as report 2007-9.)
  35. Minimal Weight and Colexicographically Minimal Integer Representations, joint work with J. Muir, J. Math. Cryptol. 1 (2007), 297–328. (Earlier version available as report 2006-11.)
  36. Maximizing the number of independent subsets over trees with bounded degree, joint work with S. Wagner, J. Graph Theory 58 (2008), 49–68. (Earlier version available as report 2007-3.)
  37. Randomness with respect to the Signed-Digit Representation, joint work with M. Archibald and V. Brattka, Fund. Inform. 83 (2008), 1–19. (Earlier version available as report 2007-13.)
  38. Positional Number Systems with Digits Forming an Arithmetic Progression, joint work with H. Prodinger and S. Wagner, Monatsh. Math. 155 (2008), 349–375, DOI 10.1007/s00605-008-0008-8. (Earlier version available as report 2007-10.)
  39. Chemical trees minimizing energy and Hosoya index, joint work with S. Wagner, J. Math. Chem. 46 (2009), 214–230, DOI 10.1007/s10910-008-9456-6. (Earlier version available as report 2008-6 and as arXiv:0804.0516v1 [math.CO].)
  40. Unbalanced digit sets and the closest choice strategy for minimal weight integer representations, joint work with J. Muir, Des. Codes Cryptogr. 52 (2009), 185–208, DOI 10.1007/s10623-009-9276-0. (Earlier version available as report 2008-5 and as Cryptology ePrint Archive, Report 2008/135.)
  41. Analysis of Complements in Multi-Exponentiation Algorithms Using Signed Digit Representations, joint work with H. Prodinger, Internat. J. Found. Comput. Sci. 20 (2009), 443–453, DOI 10.1142/S012905410900667X, (An earlier version, entitled Complements and Signed Digit Representations: Analysis of a Multi-Exponentiation-Algorithm of Wu, Lou, Lai and Chang, is available as report 2008-8 and as arXiv:0804.0733v1 [math.CO].)
  42. On a Class of Extremal Trees for Various Indices, joint work with S. Wagner, MATCH Commun. Math. Comput. Chem. 62 (2009), 437–464. Online Ressources. (Earlier version available as report 2008-15.)
  43. Redundant τ-adic Expansions II: Non-Optimality and Chaotic Behaviour, Math. Comput. Sci., DOI 10.1007/s11786-009-0014-9.(Earlier version available as report 2008-4 and as Cryptology ePrint Archive, Report 2008/153.)
  44. Graphen, Ziffern und Kryptographie, Internat. Math. Nachrichten 212 (2009), 1–10.

Accepted for publication

  1. A precise description of the p-adic valuation of the number of alternating sign matrices, joint work with H. Prodinger, to appear in Int. J. Number Theory. (Earlier version also available as report 2009-12 and arXiv:0908.0149v1 [math.NT])

Submitted

  1. Asymptotics of the extremal values of certain graph parameters in trees with bounded degree, joint work with S. Wagner, submitted. (Also available as report 2007-12.)
  2. Redundant τ-adic Expansions I: Non-Adjacent Digit Sets and their Applications to Scalar Multiplication, joint work with R. Avanzi and H. Prodinger, submitted. (Also available as report 2008-7 and as Cryptology ePrint Archive, Report 2008/148.)

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Last Modification: 2010-02-10 by Clemens Heuberger

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