@article{60491, abstract = {{We investigate generalisations of 1-factorisations and hyperfactorisations of the complete graph $K_{2n}$. We show that they are special subsets of the association scheme obtained from the Gelfand pair $(S_{2n},S_2 \wr S_n)$. This unifies and extends results by Cameron (1976) and gives rise to new existence and non-existence results. Our methods involve working in the group algebra $\mathbb{C}[S_{2n}]$ and using the representation theory of $S_{2n}$.}}, author = {{Klawuhn, Lukas-André Dominik and Bamberg, John}}, journal = {{Algebraic Combinatorics}}, number = {{3}}, pages = {{789--809}}, title = {{{On the association scheme of perfect matchings and their designs}}}, doi = {{10.5802/alco.490}}, volume = {{9}}, year = {{2026}}, } @unpublished{66642, abstract = {{In this work, we build a bridge between the Pólya--Schur program and Voiculescu's free probability theory. A cornerstone of the former is the Pólya--Benz Theorem, classifying a central family of real-root preserving operators on the space of polynomials, as those given by $f(\partial_z)$ for a Laguerre--Pólya function $f$ and the derivative operator $\partial_{z}$. We prove that any free (additive) infinitely divisible distribution can be attained as the weak limit of root distributions of Appell polynomials $f_n(\partial_z)z^n$ as $n\to\infty$, for a suitably chosen sequence $f_n$ of Laguerre--Pólya functions. Such questions on the (global) limiting distributions of real rooted polynomials belong to the active research area of finite free probability. In contrast to its standard tools, our approach allows for non-compactly supported limiting distributions, (barely) complex rooted polynomials and even provides the full microscopic description of the roots. Moreover, we extend our results to differential operators generating free multiplicative infinitely divisible distributions, to the rectangular free convolution, and to $f_n(\partial_z)p_n$ for real rooted polynomials $p_n$, implying a generalization of the recent connections between the heat flow and free Brownian motion to any free Lévy process. As corollaries, we identify free stable distributions by choosing $f_n$ to be a fixed rescaled Laguerre--Pólya function, and we prove various convergence results on the zero distributions of Jensen polynomials, e.g. the limiting root distribution of Jensen polynomial of the Riemann $Ξ$-function is given by the Cauchy distribution.}}, author = {{Campbell, Andrew and Jalowy, Jonas}}, booktitle = {{arXiv:2605.31356}}, title = {{{Pólya--Schur problems and free probability}}}, year = {{2026}}, } @article{66641, author = {{Jalowy, Jonas and Stange, Hanna}}, issn = {{0304-4149}}, journal = {{Stochastic Processes and their Applications}}, publisher = {{Elsevier BV}}, title = {{{Box-covariances of hyperuniform point processes}}}, doi = {{10.1016/j.spa.2026.104996}}, volume = {{199}}, year = {{2026}}, } @unpublished{66731, abstract = {{We generalize intersection numbers for combinatorial designs to designs in finite meet-semilattices satisfying suitable regularity conditions. While designs in regular semilattices go back to Delsarte, our regularity assumptions are weaker than his and need not give rise to an association scheme. In this framework, we extend Mendelsohn's equations, prove a generalized Singleton bound with Steiner systems as equality cases, and determine the block intersection distribution at any block of a Steiner system. In particular, this distribution is independent of the chosen block. Specializing to several classical semilattice families, our results recover a number of well-known distributions in coding and design theory. In the Hamming and the $q$-Hamming (or bilinear forms) schemes, they give the local distance distributions of MDS and MRD codes, respectively. In the Johnson and $q$-Johnson (or Graßmann) schemes, they reproduce the block intersection distribution of classical and $q$-analog Steiner systems, equivalently the distance distribution of diameter-perfect constant-weight codes and diameter-perfect constant-dimension subspace codes. For the $q$-Johnson schemes, to the best of our knowledge, this result is new. As a further illustration, we apply our theory to designs of perfect matchings. Our approach provides a unified treatment of these cases in the strongest form known in the literature, determining the distribution relative to each individual block or codeword, without averaging and without linearity or additivity assumptions. Moreover, it identifies the natural double-counting objects underlying these distributions, leading to formulas in the regularity parameters of the semilattice and avoiding the more cumbersome expressions that arise in eigenvalue-based approaches via the ambient association scheme.}}, author = {{Kiermaier, Michael and Klawuhn, Lukas-André Dominik}}, title = {{{Intersection numbers for designs in regular semilattices}}}, year = {{2026}}, } @article{56116, author = {{Glöckner, Helge and Grong, Erlend and Schmeding, Alexander}}, journal = {{Differential Geometry and its Applications}}, title = {{{Boundary values of diffeomorphisms of simple polytopes, and controllability}}}, doi = {{10.1016/j.difgeo.2026.102404}}, volume = {{104}}, year = {{2026}}, } @article{66121, author = {{Bruns, Julia and Gasteiger, Hedwig and Hallemann, Svea and Schopferer, Theresa}}, issn = {{1479-4802}}, journal = {{Research in Mathematics Education}}, pages = {{1--21}}, publisher = {{Informa UK Limited}}, title = {{{Leadership practices in implementing early mathematics education as a curriculum innovation into vocational training of early childhood education}}}, doi = {{10.1080/14794802.2026.2689902}}, year = {{2026}}, } @misc{66676, booktitle = {{Der Mathematikunterricht}}, editor = {{Büchter, Theresa and Eichler, Andreas and Binder, Karin}}, number = {{3}}, pages = {{2--5}}, publisher = {{Friedrich Verlag}}, title = {{{Simulationen in der MINT-Bildung - Impulse für den Mathematikunterricht}}}, volume = {{72}}, year = {{2026}}, } @article{66677, author = {{Büchter, Theresa and Binder, Karin and Eichler, Andreas}}, journal = {{Der Mathematikunterricht}}, number = {{3}}, pages = {{6--15}}, title = {{{Unterschiedliche Typen von Simulationen - Klassifikation, Beispiele und unterrichtlicher Einsatz}}}, volume = {{73}}, year = {{2026}}, } @article{66694, author = {{Black, Tobias and Winkler, Michael}}, issn = {{2163-2480}}, journal = {{Evolution Equations and Control Theory}}, pages = {{278--308}}, publisher = {{American Institute of Mathematical Sciences (AIMS)}}, title = {{{Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid}}}, doi = {{10.3934/eect.2026091}}, volume = {{25}}, year = {{2026}}, } @inproceedings{66759, author = {{Biehler, Rolf and Binder, Karin and Haverkamp, Michael and Kempen, Leander}}, booktitle = {{Mathematikabitur „Status Quo–Quo Vadis “: Tagungsband zur Fachtagung zum Mathematikabitur am 11./12. Februar 2025 in Dresden}}, editor = {{Barzel, Bärbel and Schnasse, Saskia and Ebers, Patrick}}, location = {{Dresden}}, pages = {{56–70}}, publisher = {{Universität Duisburg-Essen}}, title = {{{Impulse zur Stochastik in der Oberstufe}}}, year = {{2026}}, } @inbook{66842, abstract = {{AnnoPy ist ein digitales Werkzeug, um kollaborativ Texte zu lesen, zu erschließen und zu analysieren. Es ist für die Präsenzlehre konzipiert und unterstützt Lehrende dabei, den Übergang von der individuellen Auseinandersetzung mit wissenschaftlichen Texten hin zu einer kollaborativ-sozialen Aushandlung des Gelesenen in Lehrveranstaltungen zu organisieren und zu strukturieren. Im Beitrag wird das digitale kollaborative Tool AnnoPy vorgestellt und gezeigt, welche Potenziale sich für die Analyse von Daten über Lernende durch die Integration von KI-basierter Learning Analytics in das Tool ergeben. Anhand von exemplarischen Daten aus einer Vorlesung der Mathematikdidaktik wird zunächst vorgestellt, wie in AnnoPy eine algorithmisch-händische Analyse und Datenauswertung erfolgte, um dann diese Art der Auswertung mit einer KI-gestützten Auswertung, bei der ein MCP-Server eingebunden wurde, zu vergleichen.}}, author = {{Scholle, Oliver and Rezat, Sara and Rezat, Sebastian and Niehus, Dominik}}, booktitle = {{Learning Analytics, Artificial Intelligence und Data Mining in der Hochschulbildung: Beiträge zur Learning AID 2025}}, editor = {{Leschke, Jonas and Queckenberg, Robert and Persike, Malte}}, isbn = {{978-3-8376-8045-4}}, pages = {{171–182}}, publisher = {{transcript}}, title = {{{AnnoPy – Potenziale von KI-basierter Learning Analytics für die Förderung wissenschaftlicher Textkompetenz}}}, doi = {{10.14361/9783839458761}}, year = {{2026}}, } @article{66836, abstract = {{This qualitative case study investigates how automated feedback from a widely accessible digital curriculum resource influences students’ mathematics learning. Drawing on a dialogic feedback framework, the study analyzes students’ feedback processes in an ecologically valid learning context. Grounded in a sociocultural perspective, the framework integrates Carless’ dialogic conceptualization of feedback, Shute’s feedback typology, and Vergnaud’s scheme theory. Eight eighth-graders from a German secondary school worked individually on percentage problems at home, video-recorded via online conferencing. Data included screen recordings and think-aloud protocols, which were analyzed using qualitative text analysis. Results reveal large individual differences in feedback processes—students vary in when and how they access feedback messages and how they make sense of them. Successfully solving a task after feedback does not always indicate understanding; in some cases, feedback aided procedural completion without conceptual insight. The effectiveness depended on the alignment between task design, feedback message content, and students’ actual difficulties. The study concludes that qualitative analysis of feedback processes with digital technologies in ecologically valid settings is necessary to target specific student difficulties and promote learning.}}, author = {{Rezat, Sebastian}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Students’ mathematical feedback processes using a digital curriculum resource: A qualitative perspective}}}, doi = {{10.1007/s11858-026-01821-4}}, year = {{2026}}, } @article{32099, author = {{Weich, Tobias and Budde, Julia}}, journal = {{Journal of Functional Analysis}}, number = {{1}}, title = {{{Wave Front Sets of Nilpotent Lie Group Representations}}}, doi = {{ https://doi.org/10.1016/j.jfa.2024.110684}}, volume = {{288}}, year = {{2025}}, } @article{56960, author = {{Black, Tobias}}, issn = {{0893-9659}}, journal = {{Applied Mathematics Letters}}, publisher = {{Elsevier BV}}, title = {{{Absence of dead-core formations in chemotaxis systems with degenerate diffusion}}}, doi = {{10.1016/j.aml.2024.109361}}, volume = {{161}}, year = {{2025}}, } @inbook{57020, abstract = {{AbstractIn this symposium we investigate students’ agency of selecting and using (digital) resources for developing their own learning paths. For that, we first review the literature related to students’ selection and use of resources in mathematics education in different pedagogical settings (presentation 1). Second, we develop insights from the different studies that participate in this symposium (presentation 2–6), at school as well as at university level. Results show that attempts have been made to provide students opportunities to develop agency of their mathematics learning, in particular with the development and provision of numerous digital tools and learning resources at university level and related to innovative pedagogical approaches. At the same time, it is not obvious how these tools and resources help students to develop deeper conceptual understandings. Certainly, students often ‘demand’ more student-centered and autonomous education approaches (e.g., at university level), also in mathematics education. Further, it seems that authentic problem-based education approaches are more motivating for students. These ‘innovative’ approaches necessitate particular types of structure and support for students. Moreover, they require different ways of providing resources that students can and want to interact with, and that help students to navigate through the curriculum to develop their own learning paths. At the same time, teachers also need support on how to orchestrate student learning with the available resources in such environments, so to be able to attend to students’ individual needs. The symposium comprised altogether six presentations:Birgit Pepin & Sebastian Rezat: Students’ agency of selecting and using (digital) resources for developing their own learning paths: An overviewAnnalisa Cusi & Agnese I. Telloni: Learning through digital curriculum resource design: students’ reflections on their role as designersVilma Mesa, Lelia Burley-Sanford, Xinyi Hao, & Carlos Quiroz: Interactive features in university textbooks and their use by teachers and studentsSebastian Rezat: Fostering university students’ reading and understanding of mathematical text in a flipped classroom approach with a digital marking toolBirgit Pepin & Ulises Salinas: Challenge/problem-based mathematics learning at university level: The case of the modeling weekFarzad Radmehr: Problem-posing: An inclusive activity for improving teaching and learning of mathematics at university level}}, author = {{Pepin, Birgit and Rezat, Sebastian}}, booktitle = {{Recent Advances in Mathematics Textbook Research and Development}}, editor = {{Qi, Chunxia and Fan, Lianghuo and Liu, Jian and Liu, Qimeng and Dong, Lianchun}}, isbn = {{9789819784257}}, pages = {{123–126}}, publisher = {{Springer Nature}}, title = {{{Symposium—Towards innovative practices in mathematics education: Teachers’ and students’ choice and use of digital resources}}}, doi = {{10.1007/978-981-97-8426-4_17}}, year = {{2025}}, } @inbook{57022, abstract = {{AbstractEven in the digital age, learning mathematics at an academic level still requires much interaction with mathematical texts. Understanding and developing disciplinary literacy skills at all levels is an increasing matter of interest.}}, author = {{Rezat, Sebastian}}, booktitle = {{Recent Advances in Mathematics Textbook Research and Development}}, editor = {{Qi, Chunxia and Fan, Lianghuo and Liu, Jian and Liu, Qimeng and Dong, Lianchun}}, isbn = {{9789819784257}}, pages = {{133–136}}, publisher = {{Springer Nature}}, title = {{{Fostering university students’ reading and understanding of mathematical text in a flipped classroom approach with a digital marking tool}}}, doi = {{10.1007/978-981-97-8426-4_20}}, year = {{2025}}, } @article{58353, abstract = {{Abstract Statistics and machine learning are critical because they play an essential role in our everyday lives and the careers we may pursue in the future. It may be beneficial to introduce machine learning, such as decision trees (DTs), at an early stage of education. The data-based construction of DTs is an example of a machine learning process, which can be addressed in mathematics or statistics teaching because of relatively low prior knowledge requirements. This paper focuses on investigating how sixth-grade students create and evaluate data-based DTs. The basis is a teaching unit that aims to lay the foundation for machine learning and enhance students’ understanding of the process. We investigate students’ processes in detail while they build DTs with data cards about food items to predict whether a new item is recommendable. After the teaching unit, an interview study examines students’ strategies for creating decision trees. The findings contribute to understanding students’ learning processes and the challenges when working with decision trees.}}, author = {{Podworny, Susanne and Biehler, Rolf and Fleischer, Yannik}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Young students’ engagement with data to create decision trees}}}, doi = {{10.1007/s11858-024-01649-w}}, year = {{2025}}, } @article{59414, author = {{Häsel-Weide, Uta and Nührenbörger, M.}}, journal = {{Zeitschrift für Grundschulforschung}}, title = {{{Unterrichtsintegrierte Förderung von mathematischen Basiskompetenzen. Empirische Rekonstruktion interferierender Praktiken der Förderung im Mathematikunterricht der Grundschule}}}, doi = {{ https://doi.org/10.1007/s42278-025-00223-x }}, year = {{2025}}, } @article{59622, abstract = {{Abstract This study explores how high school students construct decision trees using data cards and the software CODAP (codap.concord.org) in interviews after attending a teaching unit. We conceptualized data-based decision tree construction using nine key aspects that we intended to teach, tested variations of two design elements in teaching, and analyzed the interviews qualitatively to compare student behavior to intended outcomes. We found high alignment to intentions but also deviations in data activities and informal or context-based rather than data-based reasoning. The design element of context-free (blinded) data seems to enhance data-based reasoning, while the design element of data card use showed diagnostic potential.}}, author = {{Fleischer, Yannik and Biehler, Rolf}}, issn = {{1863-9690}}, journal = {{ZDM – Mathematics Education}}, number = {{1}}, publisher = {{Springer Science and Business Media LLC}}, title = {{{Exploring students’ constructions of data-based decision trees after an introductory teaching unit on machine learning}}}, doi = {{10.1007/s11858-025-01663-6}}, volume = {{57}}, year = {{2025}}, } @unpublished{59664, abstract = {{Given a sequence of polynomials $(P_n)_{n \in \mathbb{N}}$ with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting zero distribution of $P_n$ as $\mathrm{deg}\, P_n \to \infty$. The method is based on establishing an equivalence between the existence of a limiting empirical zero distribution $\mu$ and the existence of an exponential profile $g$ associated with the coefficients of the polynomials $(P_n)_{n \in \mathbb{N}}$. The exponential profile $g$, which can be roughly described by $[z^k]P_n(z) \approx \exp(n g(k/n))$, offers a direct route to computing the Cauchy transform $G$ of $\mu$: the functions $t \mapsto tG(t)$ and $\alpha \mapsto \exp(-g'(\alpha))$ are mutual inverses. This relationship, in various forms, has previously appeared in the literature, most notably in the paper [Van Assche, Fano and Ortolani, SIAM J. Math. Anal., 1987]. As a first contribution, we present a self-contained probabilistic proof of this equivalence by representing the polynomials as generating functions of sums of independent Bernoulli random variables. This probabilistic framework naturally lends itself to tools from large deviation theory, such as the exponential change of measure. The resulting theorems generalize and unify a range of previously known results, which were traditionally established through analytic or combinatorial methods. Secondly, using the profile-based approach, we investigate how the exponential profile and the limiting zero distribution behave under certain operations on polynomials, including finite free convolutions, Hadamard products, and repeated differentiation. In particular, our approach yields new proofs of the convergence results `$\boxplus_n \to \boxplus$' and `$\boxtimes_n \to \boxtimes$', extending them to cases where the distributions are not necessarily compactly supported.}}, author = {{Jalowy, Jonas and Kabluchko, Zakhar and Marynych, Alexander}}, booktitle = {{arXiv:2504.11593}}, title = {{{Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation}}}, year = {{2025}}, }