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 8:
Number systems and fractal structures

[25]Lucia Rossi, Wolfgang Steiner and Jörg Thuswaldner, Rational self-affine tiles associated to standard and nonstandard digit system. (submitted) [bibtex]
2011
[24]Horst Brunotte, Peter Kirschenhofer and Jörg M. Thuswaldner, Shift radix systems for Gaussian integers and Peth\H o's loudspeaker, Publicationes Mathematicae Debrecen, 79(3-4), 341-356, (2011). [bibtex] [doi]
2013
[23]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]
[22]Johannes F. Morgenbesser, Wolfgang Steiner and Jörg M. Thuswaldner, Patterns in rational base number systems, The Journal of Fourier Analysis and Applications, 19(2), 225–250, (2013). [bibtex] [doi]
2014
[21]Johann Blieberger and Peter Kirschenhofer, Generalized Catalan sequences originating from the analysis of special data structures, Bulletin of the Institute of Combinatorics and its Applications, 71, 103–116, (2014). [bibtex]
[20]Peter Kirschenhofer and Jörg M. Thuswaldner, Shift radix systems - a survey, Chapter in Numeration and substitution 2012, Res. Inst. Math. Sci. (RIMS), Kyoto, B46, 1-59, (2014). [bibtex] [url]
[19]Milton Minervino and Wolfgang Steiner, Tilings for Pisot beta numeration, Indagationes Mathematicae, 25(4), 745–773, (2014). [bibtex] [doi]
[18]Milton Minervino, Rauzy fractals and tilings, PhD thesis, Montanuniversität Leoben, (2014). [bibtex] [pdf]
[17]Milton Minervino and Jörg Thuswaldner, The geometry of non-unit Pisot substitutions, Ann. Inst. Fourier, 64(4), 1373–1417, (2014). [bibtex] [doi]
2015
[16]Wolfgang Steiner and Jörg M. Thuswaldner, Rational self-affine tiles, Transactions of the American Mathematical Society, 367(11), 7863–7894, (2015). [bibtex] [doi]
2016
[15]Gregory R. Conner and Jörg M. Thuswaldner, Self-affine manifolds, Advances in Mathematics, 289, 725–783, (2016). [bibtex] [doi]
[14]Hui Rao and Shu-Qin Zhang, Space-filling curves of self-similar sets (I): iterated function systems with order structures, Nonlinearity, 29(7), 2112–2132, (2016). [bibtex] [doi]
2017
[13]Benoît Loridant and Shu-Qin Zhang, Topology of a class of p2-crystallographic replication tiles, Indagationes Mathematicae, 28(4), 805-823, (2017). [bibtex] [doi]
2018
[12]Peter Kirschenhofer and Jörg Thuswaldner, Distribution results on polynomials with bounded roots, Monatshefte für Mathematik, 185(4), 689–715, (2018). [bibtex] [doi]
[11]Benoit Loridant and Milton Minervino, Geometrical models for a class of reducible Pisot substitutions, Discrete &\ Computational Geometry, 60(4), 981–1028, (2018). [bibtex] [doi]
[10]Shu-Qin Zhang, Optimal parametrizations of a class of self-affine sets, Technical report, , (2018). (in preparation) [bibtex]
2019
[9]Valérie Berthé, Wolfgang Steiner and Jörg M. Thuswaldner, Geometry, dynamics, and arithmetic of $S$-adic shifts, Ann. Inst. Fourier (Grenoble), 69(3), 1347–1409, (2019). [bibtex] [doi]
[8]Valérie Berthé, Wolfgang Steiner, Jörg M. Thuswaldner and Reem Yassawi, Recognizability for sequences of morphisms, Ergodic Theory and Dynamical Systems, 39(11), 2896–2931, (2019). [bibtex] [doi]
[7]Xin-Rong Dai, Hui Rao and Shu-Qin Zhang, Space-filling curves of self-similar sets (II): edge-to-trail substitution rule, Nonlinearity, 32(5), 1772–1809, (2019). [bibtex] [doi]
[6]Attila Peth\H o, Jörg Thuswaldner and Mario Weitzer, The finiteness property for shift radix systems with general parameters, Integers, 19, A50,1-22, (2019). [bibtex] [pdf]
[5]Shu-Qin Zhang, Geometry and topology of self-affine tiles and Rauzy fractals, PhD thesis, Montanuniversität Leoben, (2019). [bibtex] [pdf]
2020
[4]Hui Rao and Shu-Qin Zhang, Space-filling curves of self-similar sets (III): skeletons, Fractals, 28(02), 2050028, (2020). [bibtex] [doi]
[3]J. Thuswaldner and S.-Q. Zhang, On self-affine tiles whose boundary is a sphere, Transactions of the American Mathematical Society, 373, 491–527, (2020). [bibtex]
2021
[2]J. Thuswaldner and S.-Q. Zhang, On self-affine tiles that are homeomorphic to a ball, (2021). (submitted) [bibtex]
2022
[1]Lucia Rossi and Jörg Thuswaldner, A number system with base $-\frac32$, American Mathematical Monthly, (2022). (to appear) [bibtex]