CV

Pattern Avoiding Permutations as Walks

Submitted to journal.

The Stanley-Wilf limit of the pattern 1324 is known to lie between 10.271 and 13.5. We obtain lower bounds on this limit by encoding permutations as walks in directed graphs: building a permutation by successive insertion of maxima corresponds to traversing edges, and the growth rate of walks equals the spectral radius of the adjacency matrix. For 1324, this graph is too large for direct computation, so we pass to a quotient graph with weighted edges. Conditional on a natural conjecture, this yields a lower bound of 10.418.

Pattern Avoiding Permutations Enumerated by Inversions

Discrete Mathematics & Theoretical Computer Science

Permutations are usually enumerated by size, but new results can be found by enumerating them by inversions instead, in which case one must restrict one’s attention to indecomposable permutations. In the style of the seminal paper by Simion and Schmidt, we investigate all combinations of permutation patterns of length at most 3.

Permutations with few inversions

Electron. J. Combin.

A curious generating function $S_0(x)$ for permutations of $[n]$ with exactly $n$ inversions is presented. Moreover, $(xC(x))^iS_0(x)$ is shown to be the generating function for permutations of $[n]$ with exactly $n-i$ inversions, where $C(x)$ is the generating function for the Catalan numbers.

The difficulty of beating the Taxman

Discrete Applied Mathematics

The Taxman game has proven to be hard to solve optimally, so efforts have been made to find heuristic strategies that do well in practice. We present results on the NP-hardness of a variant of the game via an equivalence to a particular kind of graph matching problem. Furthermore this equivalence is used to derive a winning strategy for all along with efficiently computable lower and upper bounds on the optimal achievable score.

Counting tournament score sequences

Proceedings of the American Mathematical Society

The score sequence of a tournament is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The problem of counting score sequences of a tournament with vertices is more than 100 years old [Quart. J. Math. 49 (1920), pp. 1–36]. In 2013 Hanna conjectured a surprising and elegant recursion for these numbers. We settle this conjecture in the affirmative by showing that it is a corollary to our main theorem, which is a factorization of the generating function for score sequences with a distinguished index. We also derive a closed formula and a quadratic time algorithm for counting score sequences.

Part-time teacher

University of Reykjavík

Taught problem-solving oriented and mathematical programming several times along with Arnar Bjarni Arnarson, and taught a handful of other courses as well.

• Problem-solving Oriented Programming (teacher, 2022, 2023, 2024, 2025, 2026)
• Programming in C++ (teacher, 2026)
• Linear Algebra for Computer Science (teacher, 2026)
• Mathematical Programming (teacher, 2022, 2023, 2024, 2025)

Part-time teacher

University of Iceland

Taught competitive programming five times as the main teacher (sometimes along with Bergur Snorrason), getting to design and plan my own course. Taught in several other courses as a teaching assistant.

• Keppnisforritun (teacher, 2019, 2020, 2022, 2023, 2025)
• Graph Theory (teaching assistant, 2022, 2024, 2025)
• Formal Languages (teaching assistant, 2025)
• Random Processes (teaching assistant, 2023)
• Numerical Analysis (teaching assistant, 2022)

PhD

University of Iceland

Combinatorics

MSc

University of Zürich

Pure Mathematics

Double BSc

University of Iceland

Mathematics, Computer Science