Joel Larsson Danielsson

activity

20142024

collaborators

7 papers

math.PR2024

Random triangulations of the d-sphere with minimum volume

Agelos Georgakopoulos, John Haslegrave, Joel Larsson Danielsson

We study a higher-dimensional analogue of the {Random Travelling Salesman Problem}: let the complete $d$ -dimensional simplicial complex $K_{n}^{d}$ on $n$ vertices be equipped with i…

math.CO2024

A concentration inequality for random combinatorial optimisation problems

Joel Larsson Danielsson

Given a finite set $S$ , i.i.d. random weights ${X_{i}}_{i \in S}$ , and a family of subsets $F \subseteq 2^{S}$ , we consider the minimum weight of an $F \in F$ : \[ M(…

math.CO2023

Minimal H-factors and covers

Lorenzo Federico, Joel Larsson Danielsson

Given a fixed small graph H and a larger graph G, an H-factor is a collection of vertex-disjoint subgraphs $H^{'} \subset G$ , each isomorphic to H, that cover the vertices of G. If G i…

math.PR2022

Polarised random k-SAT

Joel Larsson Danielsson, Klas Markström

In this paper we study a variation of the random $k$ -SAT problem, called polarized random $k$ -SAT. In this model there is a polarization parameter $p$ , and in half of the clauses e…

math.CO2019

Biased random k-SAT

Joel Larsson, Klas Markström

The basic random $k$ -SAT problem is: Given a set of $n$ Boolean variables, and $m$ clauses of size $k$ picked uniformly at random from the set of all such clauses on our variables,…

math.PR2016

Speed and concentration of the covering time for structured coupon collectors

Victor Falgas-Ravry, Joel Larsson, Klas Markström

Let $V$ be an $n$ -set, and let $X$ be a random variable taking values in the powerset of $V$ . Suppose we are given a sequence of random coupons $X_{1}, X_{2}, \dots$ , where the $X_{i}$ …

math.CO2014

The Minimum Perfect Matching in Pseudo-dimension $0 < q < 1$

Joel Larsson

It is known that for $K_{n, n}$ equipped with i.i.d. $e x p (1)$ edge costs, the minimum total cost of a perfect matching converges to $π^{2} /6$ in probability. Similar convergence has b…