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Research Areas

My research lies within Discrete Mathematics, more precisely within Combinatorics. I am interested in enumerative aspects of labelled combinatorial objects and in the complexity of combinatorial problems.
  • Enumeration: permutation patterns, generalized parking functions, patterns in trees and mappings; exact and asymptotic results, generating functions and bijections, log-concavity of combinatorial sequences

  • Complexity analysis: aspects and variants of the Permutation Pattern Matching problem; classical and parametrized complexity theory, design of (FPT)-algorithms

  • Social Choice Theory: Connection between domain restrictions and permutation patterns, likelihood of domain restrictions; combinatorial and probabilistic methods

Publications

A list of all my publications on arxiv.org can be found here.

Submitted work

  • Ascending Runs in Cayley Trees and Mappings, joint work with Alois Panholzer, preprint available here

Talks

  • Parking functions generalised to trees and mappings - enumerative and asymptotic results, Mathematics colloquium, The Open University, UK, May 2016.
  • Parking in trees and mappings - enumerative results and a phase change behaviour, Combinatorics seminar, University of Oxford, UK, March 2016.
  • Efficient Algorithms for Permutation Pattern Matching, Dagstuhl Seminar 16071 on Pattern Avoidance and Genome Sorting, Schloss Dagstuhl, Germany, February 2016.
  • An Invitation to Analytic Combinatorics and Lattice Path Counting, introductory course held together with Michael Wallner at ALEA in Europe Young Researchers' Workshop, University of Bath, UK, December 2015.
  • Log-concavity, longest increasing subsequences, and involutions, 13th Permutation Patterns conference, London, UK, June 2015.
  • The likelihood of single-peaked preference profiles: a combinatorial approach, Combinatorics Seminar, University of Florida, Gainesville, USA, January 2015.
  • A combinatorial approach to structure in preference profiles, held at seminar of the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria, January 2015.
  • The Likelihood of Structure in Preference Profiles, Workshop on Challenges in Algorithmic Social Choice, Bad Belzig, Germany.
  • Permutation Pattern Matching: From separable permutations to fixed-parameter algorithms, Combinatorics Seminar, University of Florida, Gainesville, USA, February 2014.
  • The computational landscape of permutation patterns, held at the 11th Permutation Patterns conference, University Paris Diderot, Paris, France, July 2013.
  • Parking in trees, held at 4th biennial Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM), Memorial University of Newfoundland, St. John's, Canada, June 2013.
  • Label patterns in mappings, held at the 24th International Meeting on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms, AofA 2013, Cala Galdana, Menorca, Spain, May 2013.
  • Parking arborescent, held at the Journées Aléa 2013, CIRM, Marseille, France, March 2013.
  • A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs, held at seminar of the Arbeitsgemeinschaft Diskrete Mathematik, Vienna University of Technology, Austria, October 2012.
  • A Fast Algorithm for Permutation Pattern Matching Based on Alternating Runs, held at the 10th Permutation Patterns conference, University of Strathclyde, Glasgow, Scotland, June 2012.
  • Counting multiset-permutations avoiding the pattern 122 and another pattern of length three, held at the 30th Colloquium on Combinatorics, Magdeburg, Germany, November 2011.
  • Enumerative formulae for multiset-permutations avoiding the pattern 122 and another pattern of length three,
    ÖMG-Tagung - CSASC 2011, Krems, Austria, September 2011.