# Clemens Heuberger | Publications

1. Clemens Heuberger, On a family of quintic Thue equations, J. Symbolic Comput. 26 (1998), 173–185. MR1635238 (99d:11134). Earlier version.
2. Clemens Heuberger, Attila Pethő, and Robert F. Tichy, Complete solution of parametrized Thue equations, Acta Math. Inform. Univ. Ostraviensis 6 (1998), 93–13. MR1822519 (2002h:11026). Earlier version.
3. Clemens Heuberger, On families of parametrized Thue equations, J. Number Theory 76 (1999), 45–61. MR1688196 (2000a:11045). Earlier version.
4. Clemens Heuberger and Robert F. Tichy, Effective solution of families of Thue equations containing several parameters, Acta Arith. 91 (1999), 147–163. MR1726188 (2000m:11027). Earlier version.
5. Clemens Heuberger and Maohua Le, On the generalized Ramanujan-Nagell equation $x^2+D=p^z$, J. Number Theory 78 (1999), 312–331. MR1713461 (2000f:11034). Earlier version.
6. Clemens Heuberger, On general families of parametrized Thue equations, Algebraic Number Theory and Diophantine Analysis. Proceedings of the International Conference held in Graz, Austria, August 30 to September 5, 1998 (F. Halter-Koch and R. F. Tichy, eds.), Walter de Gruyter, 2000, pp. 215–238. MR1770464 (2001f:11048). Earlier version.
7. Clemens Heuberger, Minimal expansions in redundant number systems and shortest paths in graphs, Computing 63 (1999), 341–349. MR1738715 (2001b:11008). Earlier version.
8. Clemens Heuberger, On a conjecture of E. Thomas concerning parametrized Thue equations, Acta Arith. 98 (2001), 375–394. MR1829779 (2002g:11031). Earlier version.
9. Clemens Heuberger and Helmut Prodinger, On minimal expansions in redundant number systems: Algorithms and quantitative analysis, Computing 66 (2001), 377–393. MR1842756 (2002g:11014). Earlier version.
10. Clemens Heuberger, On explicit bounds for the solutions of a class of parametrized Thue equations of arbitrary degree, Monatsh. Math. 132 (2001), 325–339. MR1844070 (2002d:11032). Earlier version.
11. Clemens Heuberger, On hamiltonian Toeplitz graphs, Discrete Math. 245 (2002), 107–125. MR1887933 (2003f:05077). Earlier version.
12. Clemens Heuberger, Attila Pethő, and Robert F. Tichy, Thomas' family of Thue equations over imaginary quadratic fields, J. Symbolic Comput. 34 (2002), 437–449. MR1937468 (2003i:11043). Earlier version.
13. Clemens Heuberger, Minimal redundant digit expansions in the Gaussian integers, J. Théor. Nombres Bordeaux 14 (2002), 517–528. MR2040691 (2005c:11012). Earlier version. Additional material.
14. Clemens Heuberger and Helmut Prodinger, Carry propagation in signed digit representations, European J. Combin. 24 (2003), 293–320. MR1969583 (2004a:68172). Earlier version.
15. Clemens Heuberger, On planarity and colorability of circulant graphs, Discrete Math. 268 (2003), 153–169. MR1983275 (2004b:05066). Earlier version.
16. Peter J. Grabner, Clemens Heuberger, and Helmut Prodinger, Subblock occurrences in signed digit representations, Glasg. Math. J. 45 (2003), 427–440. MR2005345 (2005a:11113). Earlier version.
17. Peter J. Grabner, Clemens Heuberger, and Helmut Prodinger, Distribution results for low-weight binary representations for pairs of integers, Theoret. Comput. Sci. 319 (2004), 307–331. MR2074958 (2005h:11018). Earlier version.
18. Clemens Heuberger, Alain Togbé, and Volker Ziegler, Automatic solution of families of Thue equations and an example of degree 8, J. Symbolic Comput. 38 (2004), 1145–1163. MR2093887 (2005h:11070). Earlier version.
19. Clemens Heuberger, Inverse combinatorial optimization: A survey on problems, methods, and results, J. Comb. Optim. 8 (2004), 329–361. MR2092264 (2005d:90098). Earlier version.
20. Clemens Heuberger, Minimal expansions in redundant number systems: Fibonacci bases and greedy algorithms, Period. Math. Hungar. 49 (2004), 65–89. MR2106466 (2005m:11009). Earlier version.
21. Peter J. Grabner, Clemens Heuberger, and Helmut Prodinger, Counting optimal joint digit expansions, Integers 5 (2005), no. 3, A9. MR2191755 (2006i:11008). Earlier version.
22. Clemens Heuberger, Rajendra Katti, Helmut Prodinger, and Xiaoyu Ruan, The alternating greedy expansion and applications to left-to-right algorithms in cryptography, Theoret. Comput. Sci. 341 (2005), 55–72. MR2159644 (2007d:94034). Earlier version.
23. Peter J. Grabner, Clemens Heuberger, Helmut Prodinger, and Jörg Thuswaldner, Analysis of linear combination algorithms in cryptography, ACM Trans. Algorithms 1 (2005), 123–142. MR2163134 (2006j:65425). Earlier version. Additional material.
24. Clemens Heuberger and Helmut Prodinger, Analysis of alternative digit sets for nonadjacent representations, Monatsh. Math. 147 (2006), 219–248. MR2215565 (2007g:11010). Earlier version.
25. Roberto Avanzi, Clemens Heuberger, and Helmut Prodinger, Minimality of the Hamming weight of the $\tau$-NAF for Koblitz curves and improved combination with point halving, Selected Areas in Cryptography: 12th International Workshop, SAC 2005, Kingston, ON, Canada, August 11–12, 2005, Revised Selected Papers (B. Preneel and S. Tavares, eds.), Lecture Notes in Comput. Sci., vol. 3897, Springer, Berlin, 2006, pp. 332–344. MR2241647 (2007f:94028). Earlier version.
26. Peter J. Grabner and Clemens Heuberger, On the number of optimal base 2 representations of integers, Des. Codes Cryptogr. 40 (2006), no. 1, 25–39. MR2226281 (2007f:11008). Earlier version.
27. Clemens Heuberger, All solutions to Thomas' family of Thue equations over imaginary quadratic number fields, J. Symbolic Comput. 41 (2006), 980–998. MR2251815 (2008a:11037). Earlier version. Additional material.
28. Roberto Avanzi, Clemens Heuberger, and Helmut Prodinger, Scalar multiplication on Koblitz curves. Using the Frobenius endomorphism and its combination with point halving: Extensions and mathematical analysis, Algorithmica 46 (2006), 249–270. MR2291956 (2008a:94180). Earlier version.
29. Clemens Heuberger, Parametrized Thue equations — A survey, Proceedings of the RIMS symposium “Analytic Number Theory and Surrounding Areas”, Kyoto, Oct 18–22, 2004, RIMS Kôkyûroku, vol. 1511, 2006, pp. 82–91.
30. Clemens Heuberger and Helmut Prodinger, On $\alpha$-greedy expansions of numbers, Adv. in Appl. Math. 38 (2007), 505–525. MR2311049 (2008b:11011). Earlier version.
31. Clemens Heuberger, Attila Pethő, and Robert F. Tichy, Thomas' family of Thue equations over imaginary quadratic fields. II, Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 142 (2006), 3–7. MR2373935 (2008k:11036). Earlier version.
32. Clemens Heuberger and Helmut Prodinger, The Hamming weight of the non-adjacent-form under various input statistics, Period. Math. Hungar. 55 (2007), 81–96. MR2341895 (2009b:05021). Earlier version.
33. Roberto Avanzi, Clemens Heuberger, and Helmut Prodinger, On redundant $\tau$-adic expansions and non-adjacent digit sets, Selected Areas in Cryptography: 13th International Workshop, SAC 2006, Montreal, Canada, August 2006, Revised Selected Papers (E. Biham and A. Youssef, eds.), Lecture Notes in Comput. Sci., vol. 4356, Springer, Berlin, 2007, pp. 285–301. Earlier version.
34. Clemens Heuberger, Hwang's quasi-power-theorem in dimension two, Quaest. Math. 30 (2007), 507–512. MR2368568 (2009f:60031). Earlier version.
35. Clemens Heuberger and James A. Muir, Minimal weight and colexicographically minimal integer representations, J. Math. Cryptol. 1 (2007), 297–328. MR2441062 (2010f:11014). Earlier version. Additional material.
36. Clemens Heuberger and Stephan G. Wagner, Maximizing the number of independent subsets over trees with bounded degree, J. Graph Theory 58 (2008), 49–68. MR2404041 (2009i:05178). Earlier version.
37. Margaret Archibald, Vasco Brattka, and Clemens Heuberger, Randomness with respect to the signed-digit representation, Fund. Inform. 83 (2008), 1–19. MR2389122 (2009f:68081). Earlier version.
38. Clemens Heuberger, Helmut Prodinger, and Stephan G. Wagner, Positional number systems with digits forming an arithmetic progression, Monatsh. Math. 155 (2008), 349–375. MR2461584 (2009j:11018). Earlier version.
39. Clemens Heuberger and Stephan G. Wagner, Chemical trees minimizing energy and Hosoya index, J. Math. Chem. 46 (2009), 214–230. MR2598492. Earlier version.
40. Clemens Heuberger and James A. Muir, Unbalanced digit sets and the closest choice strategy for minimal weight integer representations, Des. Codes Cryptogr. 52 (2009), 185–208. MR2496255 (2010c:11008). Earlier version.
41. Clemens Heuberger and Helmut Prodinger, Analysis of complements in multi-exponentiation algorithms using signed digit representations, Internat. J. Found. Comput. Sci. 20 (2009), 443–453. MR2533269. Earlier version.
42. Clemens Heuberger and Stephan G. Wagner, On a class of extremal trees for various indices, MATCH Commun. Math. Comput. Chem. 62 (2009), 437–464. MR2568730 (2010k:05147). Earlier version. Additional material.
43. Clemens Heuberger, Graphen, Ziffern und Kryptographie, Internat. Math. Nachrichten 212 (2009), 1–10.
44. Clemens Heuberger, Redundant $\tau$-adic expansions II: Non-optimality and chaotic behaviour, Math. Comput. Sci. 3 (2010), 141–157. MR2608292 (2011b:11012). Earlier version.
45. Clemens Heuberger and Stephan G. Wagner, Asymptotics of the extremal values of certain graph parameters in trees with bounded degree, Publ. Math. Debrecen 77 (2010), 347–367. MR2741854 (2011j:05030). Earlier version.
46. Roberto Avanzi, Clemens Heuberger, and Helmut Prodinger, Redundant $\tau$-adic expansions I: Non-adjacent digit sets and their applications to scalar multiplication, Des. Codes Cryptogr. 58 (2011), 173–202. MR2770310 (2012f:11010). Earlier version.
47. Roberto Avanzi and Clemens Heuberger, Faster and lower memory scalar multiplication on supersingular curves in characteristic three, Public Key Cryptography — PKC 2011. 14th International Conference on Practice and Theory in Public Key Cryptography, Taormina, Italy, March 6-9, 2011. Proceedings (Dario Catalano, Nelly Fazio, Rosario Gennaro, and Antonio Nicolosi, eds.), Lecture Notes in Computer Science, vol. 6571, Springer, 2011, pp. 109–127. MR2804911 (2012h:11178).
48. Clemens Heuberger and Helmut Prodinger, A precise description of the $p$-adic valuation of the number of alternating sign matrices, Int. J. Number Theory 7 (2011), 57–69. MR2776008 (2012f:11196). Earlier version.
49. Clemens Heuberger and Stephan G. Wagner, The number of maximum matchings in a tree, Discrete Math. 311 (2011), 2512–2542. MR2832150 (2012m:05172). Earlier version. Additional material.
50. Florian Heigl and Clemens Heuberger, Analysis of digital expansions of minimal weight, 23rd Intern. Meeting on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'12), DMTCS Proceedings, 2012, pp. 399–411. MR2957346.
51. Clemens Heuberger, Daniel Krenn, and Stephan Wagner, Analysis of parameters of trees corresponding to Huffman codes and sums of unit fractions, Proceedings of the Meeting on Analytic Algorithmics & Combinatorics (ANALCO), New Orleans, Louisiana, USA, January 6, 2013, SIAM, Philadelphia PA, 2013, pp. 33–42.
52. Clemens Heuberger and Daniel Krenn, Analysis of width-$w$ non-adjacent forms to imaginary quadratic bases, J. Number Theory 133 (2013), no. 5, 1752–1808. MR3007130. Earlier version.
53. Christian Elsholtz, Clemens Heuberger, and Helmut Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Trans. Inf. Theory 59 (2013), 1065–1075. MR3015716. Earlier version.
54. Clemens Heuberger and Daniel Krenn, Existence and optimality of $w$-non-adjacent forms with an algebraic integer base, Acta Math. Hungar. 140 (2013), no. 1–2, 90–104. MR3123865. Earlier version.
55. Clemens Heuberger and Daniel Krenn, Optimality of the width-$w$ non-adjacent form: General characterisation and the case of imaginary quadratic bases, J. Théor. Nombres Bordeaux 25 (2013), no. 2, 353–386. MR3228312. Earlier version.
56. Clemens Heuberger and Michela Mazzoli, Symmetric digit sets for elliptic curve scalar multiplication without precomputation, Theoret. Comput. Sci. 547 (2014), 18–33. MR3233460.
57. Clemens Heuberger and Sara Kropf, Analysis of the binary asymmetric joint sparse form, Combin. Probab. Comput. 23 (2014), 1087–1113. MR3265839. Electronic version © Cambridge University Press 2014.
58. Clemens Heuberger, Sara Kropf, and Helmut Prodinger, Asymptotic analysis of the sum of the output of transducers, 25th International Conference on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'14), DMTCS-HAL Proceedings Series, vol.~BA, 2014, pp. 145–156. MR3525971.
59. Clemens Heuberger, Sara Kropf, and Stephan Wagner, Variances and covariances in the central limit theorem for the output of a transducer, European J. Combin. 49 (2015), 167–187. MR3349532.
60. Clemens Heuberger, Sara Kropf, and Helmut Prodinger, Output sum of transducers: Limiting distribution and periodic fluctuation, Electron. J. Combin. 22 (2015), no. 2, 1–53. MR3359922.
61. Clemens Heuberger, Daniel Krenn, and Stephan Wagner, Canonical trees, compact prefix-free codes and sums of unit fractions: A probabilistic analysis, SIAM J. Discrete Math. 29 (2015), no. 3, 1600–1653. MR3391977.
62. Clemens Heuberger, Daniel Krenn, and Sara Kropf, Automata in {SageMath}—combinatorics meets theoretical computer science, Discrete Math. Theor. Comput. Sci. 18 (2016), no. 3.
63. Clemens Heuberger, Helmut Prodinger, and Stephan Wagner, The height of multiple edge plane trees, Aequationes Math. 90 (2016), 625–645. MR3500212.
64. Clemens Heuberger and Sara Kropf, On the higher dimensional quasi-power theorem and a Berry–{E}sseen inequality, Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 2016.
65. Martin Aumüller, Martin Dietzfelbinger, Clemens Heuberger, Daniel Krenn, and Helmut Prodinger, Counting zeros in random walks on the integers and analysis of optimal dual-pivot quicksort, Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 2016.
66. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, The register function and reductions of binary trees and lattice paths, Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 2016.
67. Benjamin Hackl, Clemens Heuberger, Helmut Prodinger, and Stephan Wagner, Analysis of bidirectional ballot sequences and random walks ending in their maximum, Ann. Comb. 20 (2016), 775–797. MR3572386.
68. Clemens Heuberger, Sara Kropf, and Helmut Prodinger, Analysis of carries in signed digit expansions, Monatsh. Math. 182 (2017), no. 2, 299–334. MR3600406.
69. Clemens Heuberger and Roswitha Rissner, Computing {$J$}-ideals of a matrix over a principal ideal domain, Linear Algebra Appl. 527 (2017), 12–31. MR3647467.
70. Clemens Heuberger and Stephan Wagner, On the monoid generated by a Lucas sequence, Number Theory—Diophantine Problems, Uniform Distribution and Applications. Festschrift in Honour of Robert F. Tichy’s 60th Birthday (Christian Elsholtz and Peter Grabner, eds.), Springer, 2017, pp. 281–301. MR3676406.
71. Clemens Heuberger and Michela Mazzoli, Elliptic curves with isomorphic groups of points over finite field extensions, J. Number Theory 181 (2017), 89–98. MR3689671.
72. Uta Freiberg, Clemens Heuberger, and Helmut Prodinger, Application of Smirnov words to waiting time distributions of runs, Electron. J. Combin. 24 (2017), no. 3. MR3711097.
73. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, Reductions of binary trees and lattice paths induced by the register function, Theoret. Comput. Sci. 705 (2018), 31–57. MR3721457.
74. Clemens Heuberger and Helmut Prodinger, Protection number in plane trees, Appl. Anal. Discrete Math. 11 (2017), 314–326. MR3719828.
75. Benjamin Hackl, Clemens Heuberger, Sara Kropf, and Helmut Prodinger, Fringe analysis of plane trees related to cutting and pruning, Aequationes Math. 92 (2018), 311–353. MR3773782.
76. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, Counting ascents in generalized Dyck paths, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018) (Dagstuhl, Germany) (James Allen Fill and Mark Daniel Ward, eds.), Leibniz International Proceedings in Informatics (LIPIcs), vol. 110, Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018, pp. 26:1–26:15.
77. Clemens Heuberger, Daniel Krenn, and Helmut Prodinger, Analysis of summatory functions of regular sequences: Transducer and Pascal's rhombus, Proceedings of the 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (Dagstuhl, Germany) (James Allen Fill and Mark Daniel Ward, eds.), Leibniz International Proceedings in Informatics (LIPIcs), vol. 110, Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018, pp. 27:1–27:18.
78. Clemens Heuberger and Sara Kropf, Higher dimensional quasi-power theorem and Berry–{E}sseen inequality, Monatsh. Math. 187 (2018), 293–314.
79. Martin Aumüller, Martin Dietzfelbinger, Clemens Heuberger, Daniel Krenn, and Helmut Prodinger, Dual-pivot quicksort: Optimality, analysis and zeros of associated lattice paths, Combin. Probab. Comput. (2018).
80. Roberto Avanzi, Clemens Heuberger, and Helmut Prodinger, Arithmetic of supersingular Koblitz curves in characteristic three, Cryptology ePrint Archive, Report 2010/436, 2010.
81. Benjamin Hackl, Daniel Kurz, Clemens Heuberger, Jürgen Pilz, and Martin Deutschmann, A statistical noise model for a class of Physically Unclonable Functions, arXiv:1409.8137 [stat.AP], 2014.
82. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, Ascents in non-negative lattice paths, arXiv:1801.02996 [math.CO], 2018.
83. Benjamin Hackl, Clemens Heuberger, and Stephan Wagner, Reducing simply generated trees by iterative leaf cutting, arXiv:1808.00363 [math.CO], 2018.
84. Clemens Heuberger and Daniel Krenn, Esthetic numbers and lifting restrictions on the analysis of summatory functions of regular sequences, arXiv:1808.00842 [math.CO], 2018.