Reminder

In all DK related publications, it is required to acknowledge support of the FWF. The following naming convention must be used in all cases:

    Austrian Science Fund (FWF): W1230

For example, you may include a sentence such as "The author acknowledges the support of the Austrian Science Fund (FWF): W1230." Please do not forget!

Project 5:
Digital expansions with applications in cryptography

Publications 2016

[17] Daniel Krenn, Stephan Wagner, Compositions into Powers of $b$: Asymptotic Enumeration and Parameters, Algorithmica, 75(4), 606—631, (2016).
[bib] [arXiv] [MR] [doi/article]

Publications 2015

[16] Daniel Krenn, Dimbinaina Ralaivaosaona, Stephan Wagner, Multi-Base Representations of Integers: Asymptotic Enumeration and Central Limit Theorems, Appl. Anal. Discrete Math., 9(2), 285—312, (2015).
[bib] [arXiv] [MR] [doi/article]
[15] Clemens Heuberger, Daniel Krenn, Stephan Wagner, Canonical Trees, Compact Prefix-free Codes and Sums of Unit Fractions: A Probabilistic Analysis, SIAM J. Discrete Math., 29(3), 1600—1653, (2015).
[bib] [arXiv] [MR] [doi/article]

Publications 2014

[14] Daniel Krenn, Stephan Wagner, The Number of Compositions into Powers of $b$, Chapter in 25th Int. Conf. Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'14), BA, 241-252, (2014).
[bib] [doi/article]
[13] Daniel Krenn, Dimbinaina Ralaivaosaona, Stephan Wagner, On the Number of Multi-Base Representations of an Integer, Chapter in 25th Int. Conf. Probabilistic, Combinatorial, and Asymptotic Methods for the Analysis of Algorithms (AofA'14), BA, 229-240, (2014).
[bib] [doi/article]

Publications 2013

[12] Daniel Krenn, Analysis of the Width-$w$ Non-Adjacent Form in Conjunction with Hyperelliptic Curve Cryptography and with Lattices, Theoretical Computer Science, 491, 47-70, (2013).
[bib] [arXiv] [MR] [doi/article]
[11] Daniel Krenn, Digit Expansions with Applications in Cryptography, PhD thesis, Graz, University of Technology, (2013).
[bib] [doi/article]
[10] Daniel Krenn, Jörg Thuswaldner, Volker Ziegler, On linear combinations of units with bounded coefficients and double-base digit expansions, Monatshefte für Mathematik, 171(3-4), 377-394, (2013).
[bib] [arXiv] [MR] [doi/article]
[9] Clemens Heuberger, Daniel Krenn, Optimality of the Width-$w$ Non-adjacent Form: General Characterisation and the Case of Imaginary Quadratic Bases, Journal of Théorie des Nombres de Bordeaux, 25(2), 353-386, (2013).
[bib] [arXiv] [MR] [doi/article]
[8] Clemens Heuberger, Daniel Krenn, Analysis of Width-$w$ Non-Adjacent Forms to Imaginary Quadratic Bases, Journal of Number Theory, 133(5), 1752-1808, (2013).
[bib] [arXiv] [MR] [doi/article]
[7] Clemens Heuberger, Daniel Krenn, Existence and Optimality of $w$-non-adjacent Forms with an Algebraic Integer Base, Acta Mathematica Hungarica, 140(1-2), 90-104, (2013).
[bib] [arXiv] [MR] [doi/article]
[6] Clemens Heuberger, Daniel Krenn, Stephan Wagner, Analysis of Parameters of Trees Corresponding to Huffman Codes and Sums of Unit Fractions, Chapter in Proc.\ ANALCO 2013 (Mcw.\arkus Nebel, W.\ Szpankowski, eds.), SIAM, 33-42, (2013).
[bib] [MR] [doi/article]
[5] Sophie Frisch, Daniel Krenn, Sylow $p$-groups of polynomial permutations on the integers mod $p^n$, Journal of Number Theory, 133(12), 4188-4199, (2013).
[bib] [arXiv] [MR] [doi/article]
[4] Christian Elsholtz, Clemens Heuberger, Helmut Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Transactions on Information Theory, 59, 1065-1075, (2013).
[bib] [arXiv] [MR] [doi/article]

Publications 2012

[3] Nina S. Schmuck, Stephan G. Wagner, Hua Wang, Greedy trees, caterpillars, and Wiener-type graph invariants, Chapter in Distance in Molecular Graphs --- Theory (Ivan Gutman, Boris Furtula, eds.), University of Kragujevac and Faculty of Science Kragujevac, 12, 195-214, (2012).
[bib]
[2] Nina S. Schmuck, Stephan G. Wagner, Hua Wang, Greedy trees, caterpillars, and Wiener-type graph invariants, MATCH. Communications in Mathematical and in Computer Chemistry, 68(1), 273-292, (2012).
[bib] [MR] [doi/article]

Publications 2011

[1] Eranda Çela, Nina S. Schmuck, Shmuel Wimer, Gerhard J. Woeginger, The Wiener maximum quadratic assignment problem, Discrete Optimization, 8, 411-416, (2011).
[bib] [arXiv] [MR] [doi/article]