### 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 6:

Polynomial Diophantine equations - combinatorial and number theoretic aspects

#### Publications 2015

[13] | Shift Radix Systems and Their Generalizations, PhD thesis, MU Leoben, (2015).
[bib] [doi/article] | ,

[12] | On the characterization of Pethő's Loudspeaker, Publ. Math. Debrecen, 87(1--2), (2015).
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[11] | Characterization algorithms for shift radix systems with finiteness property, Int. J. Number Theory, 11(1), 211—232, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

[10] | On shift radix systems over imaginary quadratic Euclidean domains, Acta Cybernet., 22(2), 485—498, (2015).
[bib] [MR] [doi/article] | ,

[9] | A number theoretic problem on the distribution of polynomials with bounded roots, Integers, 15, Paper No. A10, 10, (2015).
[bib] [arXiv] [MR] | ,

[8] | Erratum to: Infinite motion and 2-distinguishability of graphs and groups, J. Algebraic Combin., 41(1), 123, (2015).
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[7] | Infinite motion and 2-distinguishability of graphs and groups, J. Algebraic Combin., 41(1), 109—122, (2015).
[bib] [arXiv] [MR] [doi/article] | ,

#### Publications 2014

[6] | Endomorphism breaking in graphs, Electronic Journal of Combinatorics, 21, P1.16, 13pp., (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[5] | Distinguishing graphs with infinite motion and nonlinear growth, Ars Mathematica Contemporanea, 7(1), 201-213, (2014).
[bib] [arXiv] [MR] [doi/article] | ,

[4] | The asymptotic form of the sum $\sum_{i=0}^n i^p \binom{n+i}{i}$: two proofs, Utilitas Mathematica, 93, 3-23, (2014).
[bib] [MR] [doi/article] | ,

[3] | Shift radix systems - a survey, Chapter in Numeration and substitution 2012, Res. Inst. Math. Sci. (RIMS), Kyoto, 1-59, (2014).
[bib] [arXiv] [MR] | ,

[2] | Generalized Catalan sequences originating from the analysis of special data structures, Bull. Inst. Combin. Appl., 71, 103—116, (2014).
[bib] [MR] | ,

#### Publications 2011

[1] | Shift radix systems for Gaussian integers and Pethő's loudspeaker, Publicationes Mathematicae Debrecen, 79(3-4), 341-356, (2011).
[bib] [MR] [doi/article] | ,