Publications

2022


Cuntz, M., & Kühne, L. (2022). On arrangements of hyperplanes from connected subgraphs.

arxiv.org/abs/2208.09251

Cuntz, M. (2022). Grassmannians over rings and subpolygons.

arxiv.org/abs/2207.09359

Cuntz, M. (2022). A Greedy Algorithm to Compute Arrangements of Lines in the Projective Plane. Discrete & computational

geometry, 68(1), 107-124.

doi.org/10.1007/s00454-021-00351-y

Cuntz, M., & Ohrmann, T. (2022). Higher braidings of diagonal type.

arxiv.org/abs/2204.05720

Cuntz, M., Elia, S., & Labbé, J. P. (2022). Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids. Annals of combinatorics, 26(1).

doi.org/10.1007/s00026-021-00555-2


2021


Cuntz, M., & Holm, T. (2021). Subpolygons in conway-coxeter frieze patterns. Algebraic Combinatorics, 4(4), 741-755.

doi.org/10.5802/ALCO.180

Cuntz, M. (2021). A bound for crystallographic arrangements. Journal of algebra, 574, 50-69.

doi.org/10.1016/j.jalgebra.2021.01.028

Baur, K., Faber, E., Gratz, S., Serhiyenko, K., Todorov, G., Cuntz, M., & Plamondon, P. G. (2021). Friezes satisfying higher slk-determinants. Algebra and Number Theory, 15(1), 29-68.

doi.org/10.2140/ant.2021.15.29


2020


Cuntz, M. (2020). "Le compte est bon" lösen mit Computeralgebra. Computeralgebra Rundbrief, 67, 19-21.

fachgruppe-computeralgebra.de/data/CA-Rundbrief/car67.pdf

Cuntz, M., Holm, T., & Jørgensen, P. (2020). Frieze patterns with coefficients. Forum of Mathematics, Sigma, 8, [e17].

doi.org/10.1017/fms.2020.13

Cuntz, M., & Geis, D. (2020). Tits arrangements on cubic curves. Innov. Incidence Geom., 18(1), 7-24.

doi.org/10.2140/iig.2020.18.7

Cuntz, M., & Mücksch, P. (2020). MAT-free reflection arrangements. Electronic Journal of Combinatorics, 27(1), [P1.28].

doi.org/10.37236/8820


2019


Cuntz, M., Mühlherr, B., & Weigel, C. J. (2019). On the Tits cone of a Weyl groupoid. Communications in algebra, 47(12), 5261-5285.

doi.org/10.1080/00927872.2019.1617873

Cuntz, M., Röhrle, G., & Schauenburg, A. (2019). Arrangements of ideal type are inductively free. International Journal of Algebra and Computation, 29(5), 761-773.

doi.org/10.48550/arXiv.1711.09760

,

doi.org/10.1142/S0218196719500267

Cuntz, M., & Mücksch, P. (2019). Supersolvable simplicial arrangements. Advances in applied mathematics, 107, 32-73.

doi.org/10.48550/arXiv.1712.01605

,

doi.org/10.1016/j.aam.2019.02.008

Cuntz, M., & Holm, T. (2019). Frieze patterns over integers and other subsets of the complex numbers. Journal of Combinatorial Algebra, 3(2), 153-188.

doi.org/10.48550/arXiv.1711.03724

,

doi.org/10.4171/JCA/29

Cuntz, M. (2019). A combinatorial model for tame frieze patterns. Münster J. Math., 12(1), 49-56.

doi.org/10.48550/arXiv.1711.09687

,

doi.org/10.17879/85169763588


2018


Cuntz, M. (2018). On subsequences of quiddity cycles and Nichols algebras. Journal of algebra, 502, 315-327.

doi.org/10.1016/j.jalgebra.2018.01.028

Cuntz, M. J. (2018). (224) and (264) configurations of lines. Ars mathematica contemporanea, 14(1), 157-163.

doi.org/10.26493/1855-3974.1402.733

Bokowski, J., & Cuntz, M. (2018). Hurwitz's regular map $(3,7)$ of genus 7: a polyhedral realization. Art Discrete Appl. Math., 1(1), P1.02, 17. [e1010].

doi.org/10.26493/2590-9770.1186.258


2017


Cuntz, M. (2017). On Wild Frieze Patterns. Experimental mathematics, 26(3), 342-348.

doi.org/10.1080/10586458.2016.1172526

Cuntz, M., & Lentner, S. (2017). A simplicial complex of Nichols algebras. Mathematische Zeitschrift, 285(3-4), 647-683.

doi.org/10.1007/s00209-016-1711-0

Cuntz, M., Muhlherr, B., & Weigel, C. J. (2017). Simplicial arrangements on convex cones. Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova, 138, 147-191.

doi.org/10.4171/RSMUP/138-8


2016


Abe, T., Cuntz, M., Kawanoue, H., & Nozawa, T. (2016). Non-recursive freeness and non-rigidity. Discrete mathematics, 339(5), 1430-1449.

doi.org/10.1016/j.disc.2015.12.017

Abe, T., Barakat, M., Cuntz, M., Hoge, T., & Terao, H. (2016). The freeness of ideal subarrangements of Weyl arrangements. Journal of the European Mathematical Society, 18(6), 1339-1348.

doi.org/10.4171/JEMS/615


2015


Cuntz, M., & Geis, D. (2015). Combinatorial simpliciality of arrangements of hyperplanes. Beitrage zur Algebra und Geometrie, 56(2), 439-458.

doi.org/10.1007/s13366-014-0190-x

Cuntz, M., & Heckenberger, I. (2015). Finite Weyl groupoids. Journal fur die Reine und Angewandte Mathematik, 2015(702), 77-108.

doi.org/10.1515/crelle-2013-0033

Cuntz, M., & Hoge, T. (2015). Free but not recursively free arrangements. Proceedings of the American Mathematical Society, 143(1), 35-40.

doi.org/10.1090/s0002-9939-2014-12263-5

Cuntz, M., & Stump, C. (2015). On root posets for noncrystallographic root systems. Mathematics of computation, 84(291), 485-503.

doi.org/10.1090/s0025-5718-2014-02841-x


2014


Cuntz, M. (2014). Frieze patterns as root posets and affine triangulations. European journal of combinatorics, 42, 167-178.

doi.org/10.1016/j.ejc.2014.06.005


2012


Cuntz, M. (2012). Simplicial Arrangements with up to 27 Lines. Discrete and Computational Geometry, 48(3), 682-701.

doi.org/10.1007/s00454-012-9423-7

Cuntz, M., Ren, Y., & Trautmann, G. (2012). Strongly symmetric smooth toric varieties. Kyoto journal of mathematics, 52(3), 597-620.

doi.org/10.1215/21562261-1625208

Barakat, M., & Cuntz, M. (2012). Coxeter and crystallographic arrangements are inductively free. Advances in mathematics, 229(1), 691-709.

doi.org/10.1016/j.aim.2011.09.011

Cuntz, M., & Heckenberger, I. (2012). Finite weyl groupoids of rank three. Transactions of the American Mathematical Society, 364(3), 1369-1393.

doi.org/10.1090/S0002-9947-2011-05368-7

Cuntz, M. (2012). Klassifikation simplizialer Arrangements mit dem Computer. Computeralgebra Rundbrief, 50, 13 - 16.

fachgruppe-computeralgebra.de/data/CA-Rundbrief/car50.pdf

Cuntz, M., Andruskiewitsch, N., Heckenberger, I., & Witherspoon, S. J. (Eds.) (2012). Mini-workshop: Nichols Algebras and Weyl Groupoids. In Oberwolfach Rep. (4 ed., Vol. 9, pp. 2879-2905). (Oberwolfach Rep.).

doi.org/10.4171/OWR/2012/47


2011


Cuntz, M. (2011). Crystallographic arrangements: Weyl groupoids and simplicial arrangements. Bulletin of the London Mathematical Society, 43(4), 734-744.

doi.org/10.1112/blms/bdr009

Cuntz, M., & Heckenberger, I. (2011). Reflection groupoids of rank two and cluster algebras of type A. Journal of Combinatorial Theory. Series A, 118(4), 1350-1363.

doi.org/10.1016/j.jcta.2010.12.003

Cuntz, M. (2011). Minimal fields of definition for simplicial arrangements in the real projective plane. Innov. Incidence Geom., 12, 12.

doi.org/10.2140/iig.2011.12.49


2009


Cuntz, M., & Heckenberger, I. (2009). Weyl groupoids of rank two and continued fractions. Algebra and Number Theory, 3(3), 317-340.

doi.org/10.2140/ant.2009.3.317

Cuntz, M., & Heckenberger, I. (2009). Weyl groupoids with at most three objects. Journal of Pure and Applied Algebra, 213(6), 1112-1128.

doi.org/10.1016/j.jpaa.2008.11.009

Cuntz, M. (2009). Integral modular data and congruences. Journal of algebraic combinatorics, 29(3), 357-387.

doi.org/10.1007/s10801-008-0139-y


2008


Cuntz, M., & Goff, C. (2008). An isomorphism between the fusion algebras of V+L and type D(1) level 2.

doi.org/10.48550/arXiv.0809.5186

Cuntz, M. (2008). Fusion algebras with negative structure constants. Journal of algebra, 319(11), 4536-4558.

doi.org/10.1016/j.jalgebra.2008.02.031


2007


Cuntz, M. (2007). Fusion algebras for imprimitive complex reflection groups. Journal of algebra, 311(1), 251-267.

doi.org/10.1016/j.jalgebra.2006.10.027