Related papers: Riffle shuffles of a deck with repeated cards
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
We apply Godsil-McKay switching to the symplectic graphs over $\mathbb{F}_2$ with at least 63 vertices and prove that the 2-rank of (the adjacency matrix of) the graph increases after switching. This shows that the switched graph is a new…
In this paper I present a conjecture for a recursive algorithm that finds each permutation of combining two sets of objects (AKA the Shuffle Product). This algorithm provides an efficient way to navigate this problem, as each atomic…
In this article, we study a model of random permutations, which we call random standardized permutations, based on a sequence of i.i.d. random variables. This model generalizes others, such as the riffle-shuffle and the major-index-biased…
We consider the irreducibility of switch-based Markov chains for the approximate uniform sampling of Hamiltonian cycles in a given undirected dense graph on $n$ vertices. As our main result, we show that every pair of Hamiltonian cycles in…
We consider the problem of optimal recovery of true ranking of $n$ items from a randomly chosen subset of their pairwise preferences. It is well known that without any further assumption, one requires a sample size of $\Omega(n^2)$ for the…
The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as…
We consider a novel setting where a set of items are matched to the same set of agents repeatedly over multiple rounds. Each agent gets exactly one item per round, which brings interesting challenges to finding efficient and/or fair {\em…
We examine the problem of exactly or approximately counting all perfect matchings in hereditary classes of nonbipartite graphs. In particular, we consider the switch Markov chain of Diaconis, Graham and Holmes. We determine the largest…
We study sorting by queues that can rearrange their content by applying permutations from a predefined set. These new sorting devices are called shuffle queues and we investigate those of them corresponding to sets of permutations defining…
Sampling uniform simple graphs with power-law degree distributions with degree exponent $\tau\in(2,3)$ is a non-trivial problem. We propose a method to sample uniform simple graphs that uses a constrained version of the configuration model…
In 1967, Klarner proposed a problem concerning the existence of reflecting $n$-queens configurations. The problem considers the feasibility of placing $n$ mutually non-attacking queens on the reflecting chessboard, an $n\times n$ chessboard…
We consider a billiard in the plane with periodic configuration of convex scatterers. This system is recurrent, in the sense that almost every orbit comes back arbitrarily close to the initial point. In this paper we study the time needed…
In a previous contribution (H.J. Stoeckmann, J. Phys. A35, 5165 (2002)), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
In a synchronized network of $n$ nodes, each node will update its parameter based on the system state in a given iteration. It is well-known that the updates can converge to a fixed point if the maximum absolute eigenvalue (spectral radius)…
We calculate exact convergence times to reach random bipartite entanglement for various random protocols. The eigenproblem of a Markovian chain governing the process is mapped to a spin chain, thereby obtaining exact expression for the gap…
The approximate uniform sampling of graph realizations with a given degree sequence is an everyday task in several social science, computer science, engineering etc. projects. One approach is using Markov chains. The best available current…
We study gossip algorithms for the rumor spreading problem which asks one node to deliver a rumor to all nodes in an unknown network. We present the first protocol for any expander graph $G$ with $n$ nodes such that, the protocol informs…
Guessing games for directed graphs were introduced by Riis for studying multiple unicast network coding problems. In a guessing game, the players toss generalised dice and can see some of the other outcomes depending on the structure of an…