Benjamin Hackl

Published

  1. Benjamin Hackl and Stephan Wagner, Binomial Sums and Mellin Asymptotics with Explicit Error Bounds: A Case Study, in 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024), Dagstuhl, Germany, 2024, vol. 302, pp. 19:1–19:15.

  2. Benjamin Hackl, Andrew Luo, Stephen Melczer, Jesse Selover, and Elaine Wong, Rigorous Analytic Combinatorics in Several Variables in SageMath, Sém. Lothar. Combin., vol. 89B, no. 90, pp. 1–12, 2023.

  3. Benjamin Hackl, Alois Panholzer, and Stephan Wagner, The uncover process for random labeled trees, Matematica, vol. 2, no. 4, pp. 861–892, 2023.

  4. Benjamin Hackl, Alois Panholzer, and Stephan Wagner, Uncovering a Random Tree, in 33rd International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2022), Dagstuhl, Germany, 2022, vol. 225, pp. 10:1–10:17.

  5. Andrei Asinowski, Benjamin Hackl, and Sarah J. Selkirk, Down-step statistics in generalized Dyck paths, Discrete Math. Theor. Comput. Sci., vol. 24, no. 1, 2022.

  6. Andrei Asinowski, Cyril Banderier, and Benjamin Hackl, Flip-sort and combinatorial aspects of pop-stack sorting, Discrete Math. Theor. Comput. Sci., vol. 22, no. 2, 2021.

  7. Benjamin Hackl, A Combinatorial Identity for Rooted Labelled Forests, Aequationes Math., vol. 94, pp. 253–257, 2020.

  8. Andrei Asinowski, Cyril Banderier, Sara Billey, Benjamin Hackl, and Svante Linusson, Pop-stack sorting and its image: permutations with overlapping runs, Acta Math. Univ. Comenian. (N.S.), vol. 88, no. 3, pp. 395–402, 2019. MR4012843.

  9. Benjamin Hackl, Clemens Heuberger, and Stephan Wagner, Reducing Simply Generated Trees by Iterative Leaf Cutting, in Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Philadelphia PA, 2019, pp. 36–44. MR3909439.

  10. Andrei Asinowski, Cyril Banderier, and Benjamin Hackl, On Extremal Cases of Pop-Stack Sorting, in Proceedings of Permutation Patterns 2019 (Zurich, Switzerland), 2019, pp. 33–37.

  11. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, Reductions of binary trees and lattice paths induced by the register function, Theoret. Comput. Sci., vol. 705, pp. 31–57, 2018. MR3721457.

  12. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, Counting Ascents in Generalized Dyck Paths, in 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018), 2018, vol. 110, pp. 26:1–26:15. MR3826145.

  13. Benjamin Hackl, Clemens Heuberger, Sara Kropf, and Helmut Prodinger, Fringe analysis of plane trees related to cutting and pruning, Aequationes Math., vol. 92, pp. 311–353, 2018. MR3773782.

  14. Benjamin Hackl and Helmut Prodinger, The Necklace Process: A Generating Function Approach, Statist. Probab. Lett., vol. 142, pp. 57–61, 2018.

  15. Benjamin Hackl and Helmut Prodinger, Growing and Destroying Catalan–Stanley Trees, Discrete Math. Theor. Comput. Sci., vol. 20, no. 1, 2018.

  16. Benjamin Hackl, Sara Kropf, and Helmut Prodinger, Iterative Cutting and Pruning of Planar Trees, in Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), Philadelphia PA, 2017, pp. 66–72.

  17. Benjamin Hackl, Clemens Heuberger, Helmut Prodinger, and Stephan Wagner, Analysis of Bidirectional Ballot Sequences and Random Walks Ending in their Maximum, Ann. Comb., vol. 20, pp. 775–797, 2016. MR3572386.

  18. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, The Register Function and Reductions of Binary Trees and Lattice Paths, in Proceedings of the 27th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, 2016. MR3817527.

Preprint

  1. Benjamin Hackl, Andrew Luo, Stephen Melczer, and Éric Schost, A SageMath Package for Analytic Combinatorics in Several Variables: Beyond the Smooth Case. arXiv:2504.09790 [math.CO], 2025.

  2. Benjamin Hackl and Stephan Wagner, A computer algebra package for bivariate asymptotics with explicit error terms. arXiv:2403.09408v3 [math.CO], 2025.

  3. Benjamin Hackl, Clemens Heuberger, and Helmut Prodinger, Ascents in Non-Negative Lattice Paths. arXiv:1801.02996 [math.CO], 2018.

Software

  2. Benjamin Hackl, Andrew Luo, Stephen Melczer, Jesse Selover, and Elaine Wong, sage_acsv – a SageMath package for analytic combinatorics in several variables. 2023.

  3. Benjamin Hackl, Clemens Heuberger, and Daniel Krenn, Asymptotic Expansions in SageMath, module in SageMath 6.10. https://github.com/sagemath/sage/issues/17601, 2015.

Short Notes, Technical Reports, and Other Publications

  1. Benjamin Hackl and Helmut Prodinger, A hypergeometric proof for a binomial identity related to 1/\pi. arXiv:1907.08680 [math.NT], 2019.

  2. Benjamin Hackl, Daniel Kurz, Clemens Heuberger, Jürgen Pilz, and Martin Deutschmann, A Statistical Noise Model for a Class of Physically Unclonable Functions. arXiv:1409.8137 [stat.AP], 2014.

Theses