Publications Discrete Mathematics

2021

2020

  • Clemens Heuberger and Daniel Krenn.  Asymptotic Analysis of Regular Sequences. Algorithmica, 82(3):429–508, 2020.
  • Daniel Krenn, Vorapong Suppakitpaisarn, and Stephan Wagner.  On the minimal Hamming weight of a multi-base representation. Journal of Number Theory, 208:168–179, 2020.
  • Günter Maresch, Ingrid Vukusic, Alexandra Dankl, and Andreas Tiefgraber. NEU seit November 2020: Online-Suche von IBDG-Beiträgen. Informationsblätter der Geometrie, 39(2):4–5, 2020.
  • Gisbert Wüstholz and Clemens Fuchs. Algebra. 2020.

2019

2018

  • K.C Chim, I Pink, and V Ziegler.  On a variant of Pillai’s problem II. Journal of Number Theory, 183:269–290, 2018.
  • Kwok Chi Chim and Volker Ziegler. On Diophantine Equations involving sums of Fibonacci numbers and powers of 2. INTEGERS, 2018.
  • Clemens Fuchs, Christoph Hutle, and Florian Luca. Diophantine triples in linear recurrences of Pisot type. Research in Number Theory, pages 4:29, 2018.
  • Clemens Fuchs, Vincenzo Mantova, and Umberto Zannier. On fewnomials, integral points, and a toric version of Bertini’s theorem. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, pages 107–134, 2018.
  • Clemens Heuberger, Daniel Krenn, and Helmut Prodinger.  Analysis of Summatory Functions of Regular Sequences: Transducer and Pascal’s Rhombus. In Proceedings of the 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, volume 110, 27:1–27:18. 2018.
  • D Krenn and Volker Ziegler.  Non-minimality of the width-ω non-adjacent form in conjunction with trace one τ-adic digit expansions and Koblitz curves in characteristic two. Mathematics of Computation, 87(310):821–854, 2018.
  • Istvan Pink and Volker Ziegler. Effective Resolution of Diophantine equations of the form $u_n+u_m=wp_1^z_1\dots p_s^z_s$. Monatshefte für Mathematik, pages 103–131, 2018.
  • Arne Winterhof, Oguz Yala, and Volker Ziegler. Non-Existence of some nearly perfect sequences, near Buston-Hadamard matrices, and near Conference matrices. Mathematics in Computer Science, pages 465–471, 2018.

2017

2016

2015

  • Guy Barat, Peter J.Grabner, and Peter Hellekalek. Pierre Liardet (1943-2014) In Memoriam. Newsletter of the European Mathematical Society, pages 52–58, 2015.
  • Clemens Fuchs and Duc Hiep Pham. Commutative algebraic groups and p-adic linear forms. Acta Arithmetica, pages 115–147, 2015.
  • Clemens Fuchs and Duc Hiep Pham. The p-adic analytic subgroup theorem revisited. p-Adic Number, Ultrametric Analysis and Applications, pages 143–156, 2015.
  • Clemens Heuberger, Daniel Krenn, and Stephan Wagner.  Canonical Trees, Compact Prefix-free Codes and Sums of Unit Fractions: A Probabilistic Analysis. SIAM Journal on Discrete Mathematics, 29(3):1600–1653, 2015.
  • Daniel Krenn, Dimbinaina Ralaivaosaona, and Stephan Wagner.  Multi-Base Representations of Integers: Asymptotic Enumeration and Central Limit Theorems. Applicable Analysis and Discrete Mathematics, 9(2):285–312, 2015.
  • Gerhard Larcher and Wolfgang Ch Schmid. Harald Niederreiter at 70. Uniform Distribution Theory, pages i–v, 2015.

2014

  • Clemens Fuchs. On Some Applications of Diophantine Approximations. 2014.
  • Clemens Fuchs and Gisbert Wüstholz. Übungen zur Algebra. 2014.
  • Clemens Fuchs and Umberto Zannier.  Integral points on curves: Siegel’s theorem after Siegel’s proof. 2014.
  • Daniel Krenn, Dimbinaina Ralaivaosaona, and Stephan Wagner. On the Number of Multi-Base Representations of an Integer. In 25th International Conference on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA’14), volume BA, 229–240. 2014.
  • Daniel Krenn and Stephan Wagner. The Number of Compositions into Powers of $b$. In 25th International Conference on Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA’14), volume BA, 241–252. 2014.

2013

2012

  • Andrej Dujella and Clemens Fuchs. On a problem of Diophantus for rationals. JOURNAL OF NUMBER THEORY, pages 2075–2083, 2012.
  • Clemens Fuchs and T.N. Shorey. Divisibility properties of hypergeometric polynomials. Journal of Combinatorics and Number Theory, pages 1–10, 2012.
  • Clemens Fuchs and Umberto Zannier. Composite rational functions expressible with few terms. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, pages 175–208, 2012.
  • P.J. Grabner, Peter Hellekalek, and P Liardet. The dynamical point of view of low-discrepancy sequences. Uniform Distribution Theory, pages 11–70, 2012.
  • Peter Hellekalek and P Kritzer. On the diaphony of some finite hybrid point sets. Acta Arithmetica, pages 257–282, 2012.
  • Peter Hellekalek and Peter Kritzer. Dyaphony of some hybrid point sets. Acta Arithmetica, 2012.
  • Florian Pausinger and Wolfgang Ch Schmid. On the Asymptotics of a Lower Bound for the Diaphony of Generalized van der Corput Sequences. 2012.

2011

  • Clemens Fuchs.  Angle trisection with Origami and related topics. ELEMENTE DER MATHEMATIK, 66(3):121–131, 2011.
  • Clemens Fuchs and Attila Pethö. COMPOSITE RATIONAL FUNCTIONS HAVING A BOUNDED NUMBER OF ZEROS AND POLES. Proceedings of the American Mathematical Society, 139(1):31–38, 2011.
  • Clemens Fuchs, Rafael von Känel, and Gisbert Wüstholz.  An effective Shafarevich theorem for elliptic curves. Acta Arithmetica, 148(2):189–203, 2011.
  • Peter Hellekalek. Hybrid function systems in the theory of uniform distribution of sequences. In Proceedings Monte Carlo and Quasi-Monte Carlo Methods. 2011.
  • Peter Hellekalek and Harald Niederreiter. Constructions of uniformly distributed sequences using the b-adic method. Uniform Distribution Theory, pages 185–200, 2011.
  • Florian Pausinger and Wolfgang Ch Schmid. A Lower Bound for the Diaphony of Generalised Van Der Corput Sequences in Arbitrary Base b. Uniform Distribution Theory, pages 31–46, 2011.

2010

  • Henri Faure, Friedrich Pillichshammer, Gottlieb Pirsic, and Wolfgang Ch Schmid. L_2 discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Acta Arithmetica, pages 395–418, 2010.
  • Peter Hellekalek. A notion of diaphony based on p-adic arithmetic. Acta Arithmetica, pages 273–284, 2010.
  • Florian Pausinger and Wolfgang Ch Schmid. A good permutation for one-dimensional diaphony. Monte Carlo Methods and Applications, pages 307–322, 2010.
  • Rudolf Schürer and Wolfgang Ch Schmid.  MinT – Architecture and applications of the (t, m, s)-net and OOA database. Mathematics and Computers in Simulation, pages 1124–1132, 2010.

2009

2008

  • Andrej Dujella, Clemens Fuchs, and Florian Luca. A polynomial variant of a problem of diophantus for pure powers. International Journal of Number Theory, 4(1):57–71, 2008.
  • Clemens Fuchs, Florian Luca, and Laszlo Szalay. Diophantine triples with values in binary recurrences. Annali della Scuola normale superiore di Pisa – Classe di scienze, 7(4):579–608, 2008.
  • Clemens Fuchs, Attila Pethö, and Robert F. Tichy. On the Diophantine equation G(n)(x) = G(m)(y) with Q(x, y)=0. 2008.
  • Aicke Hinrichs, Friedrich Pillichshammer, and Wolfgang Ch Schmid. Tractability properties of the weighted star discrepancy. Journal of Complexity, pages 134–143, 2008.

2007

  • Josef Dick, Peter Kritzer, Friedrich Pillichshammer, and Wolfgang Ch Schmid. On the existence of higher order polynomial lattices based on a generalized figure of merit. Journal of Complexity, pages 581–593, 2007.
  • Andrej Dujella, Alan Filipin, and Clemens Fuchs. Effective solution of the D(-1)-quadruple conjecture. Acta Arithmetica, 128(4):319–338, 2007.
  • Clemens Fuchs and Borka Jadrijevic.  On a parametric family of Thue inequalities over function fields. Mathematical Proceedings of the Cambridge Philosophical Society, 143:9–23, 2007.
  • Peter Hellekalek. Uniform Distribution of Sequences and a p-adic function system. Preprint, 2007.
  • Wolfgang Ch Schmid and Horst Trinker.  On linear programming bounds for nets. PAMM : Proceedings in Applied Mathematics and Mechanics, pages 1022603–1022604, 2007.

2006

2005

  • Jürgen Bierbrauer and Wolfgang Ch Schmid. An asymptotic Gilbert–Varshamov bound for (t,m,s)-nets. INTEGERS, 2005.
  • Andrej Dujella and Clemens Fuchs.  Complete solution of a problem of Diophantus and Euler. Journal of the London Mathematical Society, 71:33–52, 2005.
  • Clemens Fuchs. Diophantine problems in linear recurrences via the Subspace Theorem. INTEGERS, 2005.
  • Clemens Fuchs. Upper Bounds for the Solutions of Diophantine problems: Habilitation thesis. 2005.
  • Clemens Fuchs and Attila Pethö. Effective Bounds for the zeros of linear recurrences in function fields. J. Théorie Nombres Bordeaux, pages 749–766, 2005.
  • Wolfgang Ch Schmid and Rudolf Schürer. Shift-Nets and Salzburg Tables: Power Computing in Number-Theoretical Numerics. 2005.

2004

2003

  • A Dujella and Clemens Fuchs. A polynomial variant of a problem of Diophantus and Euler. Rocky Mountain Journal of Mathematics, 33(3):797–811, 2003.
  • Karl Entacher, Thomas Schell, Wolfgang Ch Schmid, and Andreas Uhl. Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique. International Journal of Parallel, Emergent and Distributed Systems, pages 13–26, 2003.
  • C Fuchs and RF Tichy. Perfect powers in linear recurring sequences. Acta Arithmetica, 107(1):9–25, 2003.
  • Clemens Fuchs. An upper bound for the G.C.D. of two linear recurrences. Mathematica Slovaca, pages 21–42, 2003.
  • Clemens Fuchs. Polynomial-exponential equations and linear recurrences. GLASNIK MATEMATICKI, pages 233–252, 2003.
  • Clemens Fuchs, Attila Pethö, and Robert F. Tichy. On the Diophantine equation G(n)(x)=G(m)(P(x)): Higher-order recurrences. Transactions of the American Mathematical Society, 355(11):4657–4681, 2003.
  • Peter Hellekalek and Stefan Wegenkittl. Empirical evidence concerning AES. ACM transactions on modeling and computer simulation, pages 322–333, 2003.

2002

  • J. Bierbrauer, Y. Edel, and Wolfgang Ch Schmid. Coding-theoretic constructions for (t,m,s)-nets and ordered orthogonal arrays. Journal of Combinatorial Designs, pages 403–418, 2002.
  • Andrej Dujella, Clemens Fuchs, and Robert F. Tichy. Diophantine m-tuples for linear polynomials. Periodica Mathematica Hungarica, 45(1-2):21–33, 2002.
  • Clemens Fuchs. Quantitative finiteness results for Diophantine equations: PhD thesis. 2002.
  • Clemens Fuchs, Attila Pethö, and Robert F. Tichy.  On the diophantine equation G(n)(x) = G(m)(P(x)). Monatshefte für Mathematik, 137(3):173–196, 2002.
  • Peter Hellekalek. Digital (t,m,s)-nets and the spectral test. Acta Arithmetica, pages 197–204, 2002.

2001

  • C Lecot and Wolfgang Ch Schmid. Particle approximation of convection-diffusion equations. Mathematics and Computers in Simulation, pages 125–132, 2001.
  • Gottlieb Pirsic and Wolfgang Ch Schmid. Calculation of the Quality Parameter of Digital Nets and Application to Their Construction. Journal of Complexity, pages 827–839, 2001.
  • Wolfgang Ch Schmid. Projections of digital nets and sequences. Mathematics and Computers in Simulation, pages 243–251, 2001.
  • Wolfgang Ch Schmid and Andreas Uhl. Techniques for parallel quasi-Monte Carlo integration with digital sequences and associated problems. Mathematics and Computers in Simulation, pages 253–261, 2001.

2000

  • Karl Entacher, Wolfgang Ch Schmid, and Andreas Uhl. Parallel Monte Carlo and quasi-Monte Carlo integration: the Leap-Frog case. 2000.
  • Clemens Fuchs. Algebraisch-geometrische Codes: Diploma thesis. 2000.
  • Gerhard Larcher, Wolfgang Ch Schmid, and Reinhard Wolf. On the approximation of certain mass distributions appearing in distance geometry. Acta Mathematica Hungarica, pages 295–316, 2000.

1999 and earlier

  • Peter Hellekalek. Kryptologie. 1999.
  • Peter Hellekalek. On the assessment of random and quasi-random point sets. 1999.
  • Peter Hellekalek. Vorsicht: Zufallszahlen. IMN Internationale Mathematische Nachrichten, pages 17–24, 1999.
  • Wolfgang Ch Schmid and Andreas Uhl. Parallel quasi-Monte Carlo integration using leaped (t,s)-sequences. 1999.
  • Peter Hellekalek. Good random number generators are (not so) easy to find. Mathematics and Computers in Simulation, pages 485–505, 1998.
  • Peter Hellekalek. A note on pseudorandom number generators. Eurosim, pages 8–10, 1997.
  • Peter Hellekalek and Hannes Leeb. Dyadic diaphony. Acta Arithmetica, pages 187–196, 1997.
  • Wolfgang Ch Schmid and Reinhard Wolf. Bounds for digital nets and sequences. Acta Arithmetica, pages 377–399, 1997.
  • Dominik Brunner, Gerhard Larcher, and Wolfgang Ch Schmid. PANUMIWAL: a system for the parallel numerical integration of high-dimensional functions. 1996.
  • Gerhard Larcher, A Lauß, S Niederreiter, and Wolfgang Ch Schmid. Optimal polynomials for (t,m,s)-nets and numerical integration of multivariate Walsh series. SIAM Journal on Numerical Analysis, pages 2239–2253, 1996.
  • Gerhard Larcher, S Niederreiter, and Wolfgang Ch Schmid. Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration. Monatshefte für Mathematik, pages 231–253, 1996.
  • Gerhard Larcher, Wolfgang Ch Schmid, and Reinhard Wolf. Quasi-Monte Carlo Methods for the Numerical Integration of Multivariate Walsh series. Mathematical and Computer Modelling, pages 55–67, 1996.
  • G Mullen and Wolfgang Ch Schmid. An equivalence between (t,m,s)-nets and strongly orthogonal hypercubes. Journal of Combinatorial Theory (A), pages 164–174, 1996.
  • Wolfgang Ch Schmid. An algorithm to determine the quality parameter of binary nets, and the new shift-method. 1996.
  • Peter Hellekalek. General discrepancy estimates III: the Erdös-Turán-Koksma inequality for the Haar function system. Monatshefte für Mathematik, pages 25–45, 1995.
  • Gerhard Larcher, A Lauß, and Wolfgang Ch Schmid. Classical number-theoretical integration methods and the Walsh series lattice rule: a comparison. 1995.
  • Gerhard Larcher and Wolfgang Ch Schmid. On the numerical integration of high-dimensional Walsh series by quasi-Monte Carlo methods. Mathematics and Computers in Simulation, pages 127–134, 1995.
  • Peter Hellekalek. General discrepancy estimates II: the Haar function system. Acta Arithmetica, pages 313–322, 1994.
  • Peter Hellekalek. General discrepancy estimates: the Walsh function system. Acta Arithmetica, pages 209–218, 1994.
  • Gerhard Larcher and Wolfgang Ch Schmid. Numerical integration of multivariate Walsh series by means of different (t,m,s)-nets. 1994.
  • Gerhard Larcher, Wolfgang Ch Schmid, and Reinhard Wolf. Representation of functions as Walsh series to different bases and an application to the numerical integration of high-dimensional Walsh series. MATHEMATICS OF COMPUTATION, pages 701–716, 1994.
  • Peter Hellekalek and Gerhard Larcher. On the boundedness of Weyl sums. Monatshefte für Mathematik, pages 1999ff, 1992.
  • Peter Hellekalek and Gerhard Larcher. Weyl sums over irrational rotations. Grazer Mathematische Berichte, pages 29–43, 1992.
  • Peter Hellekalek and Gerhard Larcher. Functions with bounded remainder. Annales de l’Insitut Fourier, pages 17ff, 1989.
  • Peter Hellekalek and Gerhard Larcher. On Weyl sums and skew products over irrational rotations. Theoretical Computer Science, pages 189ff, 1989.
  • Peter Hellekalek. Ergodicity of a class of cylinder flows related to irregularities of distribution. COMPOSITIO MATHEMATICA, pages 129ff, 1987.
  • Peter Hellekalek and Gerhard Larcher. On the ergodicity of a class of skew products. Israel Journal of Mathematics, pages 301–310, 1986.
  • Peter Hellekalek. Regularities in the distribution of special sequences. JOURNAL OF NUMBER THEORY, pages 41ff, 1984.
  • Peter Hellekalek. On regularities of the distribution of special sequences. Monatshefte für Mathematik, pages 291ff, 1980.
  • Peter Hellekalek. Zur Konvergenz der Ln – Diskrepanz gegen die extreme Diskrepanz. Monatshefte für Mathematik, pages 1–6, 1979.
  • Peter Hellekalek. Über das Wachstum von Ln-Normen. Sitzungsberichte der Österreichischen Akademie der Wissenschaften, pages 189ff, 1979.