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

[17]Daniel Krenn and Stephan Wagner, Compositions into Powers of $b$: Asymptotic Enumeration and Parameters, Algorithmica, 75(4), 606–631, (2016). [bibtex] [doi]
[16]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). [bibtex] [doi]
[15]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). [bibtex] [doi]
[14]Daniel Krenn and 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). [bibtex] [url]
[13]Daniel Krenn, Dimbinaina Ralaivaosaona and 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). [bibtex] [url]
[12]Daniel Krenn, Digit Expansions with Applications in Cryptography, PhD thesis, Graz, University of Technology, (2013). [bibtex] [url]
[11]Daniel Krenn, Jörg Thuswaldner and Volker Ziegler, On linear combinations of units with bounded coefficients and double-base digit expansions, Monatshefte für Mathematik, 171(3-4), 377-394, (2013). [bibtex] [doi]
[10]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). [bibtex] [doi]
[9]Clemens Heuberger and Daniel Krenn, Existence and Optimality of $w$-non-adjacent Forms with an Algebraic Integer Base, Acta Mathematica Hungarica, 140(1-2), 90-104, (2013). [bibtex] [doi]
[8]Clemens Heuberger and 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). [bibtex] [url]
[7]Clemens Heuberger and Daniel Krenn, Analysis of Width-$w$ Non-Adjacent Forms to Imaginary Quadratic Bases, Journal of Number Theory, 133(5), 1752-1808, (2013). [bibtex] [doi]
[6]Clemens Heuberger, Daniel Krenn and Stephan Wagner, Analysis of Parameters of Trees Corresponding to Huffman Codes and Sums of Unit Fractions, Chapter in Proc. ANALCO 2013 (Markus Nebel, W. Szpankowski, eds.), SIAM, 33-42, (2013). [bibtex] [doi]
[5]Sophie Frisch and Daniel Krenn, Sylow $p$-groups of polynomial permutations on the integers mod $p^n$, Journal of Number Theory, 133(12), 4188-4199, (2013). [bibtex] [doi]
[4]Christian Elsholtz, Clemens Heuberger and Helmut Prodinger, The number of Huffman codes, compact trees, and sums of unit fractions, IEEE Transactions on Information Theory, 59, 1065-1075, (2013). [bibtex] [doi]
[3]Nina S. Schmuck, Stephan G. Wagner and 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). [bibtex]
[2]Nina S. Schmuck, Stephan G. Wagner and Hua Wang, Greedy trees, caterpillars, and Wiener-type graph invariants, MATCH. Communications in Mathematical and in Computer Chemistry, 68(1), 273-292, (2012). [bibtex] [pdf]
[1]Eranda Çela, Nina S. Schmuck, Shmuel Wimer and Gerhard J. Woeginger, The Wiener maximum quadratic assignment problem, Discrete Optimization, 8, 411-416, (2011). [bibtex] [doi]