Related papers: Riffle shuffles of a deck with repeated cards
We study a new reconfiguration problem inspired by classic mechanical puzzles: a colored token is placed on each vertex of a given graph; we are also given a set of distinguished cycles on the graph. We are tasked with rearranging the…
The Fisher-Yates shuffle is a well-known algorithm for shuffling a finite sequence, such that every permutation is equally likely. Despite its simplicity, it is prone to implementation errors that can introduce bias into the generated…
In [5], Holroyd, Levine, M\'esz\'aros, Peres, Propp and Wilson characterize recurrent chip-and-rotor configurations for strongly connected digraphs. However, the number of steps needed to recur, and the number of orbits is left open for…
We consider the chessboard pebbling problem analyzed by Chung, Graham, Morrison and Odlyzko [3]. We study the number of reachable configurations $G(k)$ and a related double sequence $G(k,m)$. Exact expressions for these are derived, and we…
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…
Swish is a card game in which players are given cards having symbols (hoops and balls), and find a valid superposition of cards, called a "swish." Dailly, Lafourcade, and Marcadet (FUN 2024) studied a generalized version of Swish and showed…
The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…
In a previous work, the first and third authors studied a random knot model for all two-bridge knots using billiard table diagrams. Here we present a closed formula for the distribution of the crossing numbers of such random knots. We also…
In this paper we study the randomly edge colored graph that is obtained by adding randomly colored random edges to an arbitrary randomly edge colored dense graph. In particular we ask how many colors and how many random edges are needed so…
We use the Chebyshev knot diagram model of Koseleff and Pecker in order to introduce a random knot diagram model by assigning the crossings to be positive or negative uniformly at random. We give a formula for the probability of choosing a…
Many applications in network analysis require algorithms to sample uniformly at random from the set of all graphs with a prescribed degree sequence. We present a Markov chain based approach which converges to the uniform distribution of all…
Since the seminal work of Sinai one studies chaotic properties of planar billiards tables. Among them is the study of decay of correlations for these tables. There are examples in the literature of tables with exponential and even…
We apply periodic orbit theory to a quantum billiard on a torus with a variable number N of small circular scatterers distributed randomly. Provided these scatterers are much smaller than the wave length they may be regarded as sources of…
The switching model is a Markov chain approach to sample graphs with fixed degree sequence uniformly at random. The recently invented Curveball algorithm for bipartite graphs applies several switches simultaneously (`trades'). Here, we…
The function that counts the number of ways to place nonattacking identical chess or fairy chess pieces in a rectangular strip of fixed height and variable width, as a function of the width, is a piecewise polynomial which is eventually a…
We consider a strictly convex billiard table with $C^2$ boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation…
In this paper we extend the investigation into the transition from sure to probabilistic sniping as introduced in Menkveld and Zoican \cite{mz2017}. In that paper, the authors introduce a stylized version of a competitive game in which high…
A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the…
Given a graph on $n$ vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length $n$ visiting each vertex once and with pairwise different colours on the edges. Similarly (for even $n$) a rainbow…