Zobrazeno 1 - 10
of 26
pro vyhledávání: '"Thörnblad, Erik"'
We investigate the existence of maximal collections of mutually noncrossing $k$-element subsets of $\left\{ 1, \dots, n \right\}$ that are invariant under adding $k\pmod n$ to all indices. Our main result is that such a collection exists if and only
Externí odkaz:
http://arxiv.org/abs/1808.03556
Autor:
Thörnblad, Erik, Zimmermann, Jakob
Publikováno v:
Journal of Integer Sequences, Vol 21, 2018
Given any polynomial $p$ in $C[X]$, we show that the set of irreducible matrices satisfying $p(A)=0$ is finite. In the specific case $p(X)=X^2-nX$, we count the number of irreducible matrices in this set and analyze the arising sequences and their as
Externí odkaz:
http://arxiv.org/abs/1701.03699
Autor:
Thörnblad, Erik
Motivated by known results for finite tournaments, we define and study the score functions of tournament kernels and the degree distributions of tournament limits. Our main theorem completely characterises those distributions that appear as the degre
Externí odkaz:
http://arxiv.org/abs/1611.09579
Autor:
Gabrysch, Katja, Thörnblad, Erik
The greedy walk is a deterministic walk that always moves from its current position to the nearest not yet visited point. In this paper we consider the greedy walk on an inhomogeneous Poisson point process on the real line. Our primary interest is wh
Externí odkaz:
http://arxiv.org/abs/1611.09568
Autor:
Thörnblad, Erik
The converse of a tournament is obtained by reversing all arcs. If a tournament is isomorphic to its converse, it is called self--converse. Eplett provided a necessary and sufficient condition for a sequence of integers to be realisable as the score
Externí odkaz:
http://arxiv.org/abs/1606.02081
Autor:
Thörnblad, Erik
Landau \cite{Landau1953} showed that a sequence $(d_i)_{i=1}^n$ of integers is the score sequence of some tournament if and only if $\sum_{i\in J}d_i \geq \binom{|J|}{2}$ for all $J\subseteq \{1,2,\dots, n\}$, with equality if $|J|=n$. Moon \cite{Moo
Externí odkaz:
http://arxiv.org/abs/1605.06407
Autor:
Thörnblad, Erik
Publikováno v:
European Journal of Combinatorics, Volume 67, January 2018, Pages 96-125
The theory of tournament limits and tournament kernels (often called graphons) is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We prove tha
Externí odkaz:
http://arxiv.org/abs/1604.04271
Publikováno v:
Stochastic Models Vol. 32 Iss. 4 (2016) 289-305
We study the limiting degree distribution of the vertex splitting model introduced in \cite{DDJS:2009}. This is a model of randomly growing ordered trees, where in each time step the tree is separated into two components by splitting a vertex into tw
Externí odkaz:
http://arxiv.org/abs/1511.02332
Autor:
Thörnblad, Erik
Publikováno v:
J. Appl. Probab. Volume 53, Number 3 (2016), 914-924
We study a P\'olya-type urn model defined as follows. Start at time 0 with a single ball of some colour. Then, at each time n>0, choose a ball from the urn uniformly at random. With probability 1/2
Externí odkaz:
http://arxiv.org/abs/1506.05862
Autor:
Thörnblad, Erik
Publikováno v:
Internet Math. Vol. 11 Iss. 3 (2015) 289-305
We study a discrete-time duplication-deletion random graph model and analyse its asymptotic degree distribution. The random graphs consists of disjoint cliques. In each time step either a new vertex is brought in with probability $0
Externí odkaz:
http://arxiv.org/abs/1408.4268