相关论文: Counting the Number of Site Swap Juggling Patterns…

The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…

We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…

We study how many riffle shuffles are required to mix n cards if only certain features of the deck are of interest, e.g. suits disregarded or only the colors of interest. For these features, the number of shuffles drops from 3/2 log_2(n) to…

A triangulation of a point configuration is regular if it can be given by a height function, that is every point gets lifted to a certain height and projecting the lower convex hull gives the triangulation. Checking regularity of a…

We introduce numbers depending on three parameters which we call skyscraper numbers. We discuss properties of these numbers and their relationship with Stirling numbers of the first kind, and we also introduce a skyscraper sequence.

New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…

History Matching is a technique used to calibrate complex computer models, that is, finding the input settings which lead to the simulated output matching up with real world observations. Key to this technique is the construction of…

In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…

A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations…

Consider a configuration of pebbles distributed on the vertices of a connected graph of order $n$. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles…

The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to…

We classify flips of buildings arising from non-degenerate unitary spaces of dimension at least 4 over finite fields of odd characteristic in terms of their action on the underlying vector space. We also construct certain geometries related…

We study empirical statistical and gap distributions of several important tilings of the plane. In particular, we consider the slope distributions, the angle distributions, pair correlation, squared-distance pair correlation, angle gap…

Site-directed insertion is an overlapping insertion operation that can be viewed as analogous to the overlap assembly or chop operations that concatenate strings by overlapping a suffix and a prefix of the argument strings. We consider…

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…

Finding all the words on a Boggle board is a classic computer programming problem. With a fast Boggle solver, local optimization techniques such as hillclimbing and simulated annealing can be used to find particularly high-scoring boards.…

We analyze the computational complexity of the problem of deciding whether, for a given simple game, there exists the possibility of rearranging the participants in a set of $j$ given losing coalitions into a set of $j$ winning coalitions.…

Let G be a graph with a distribution of pebbles on its vertices. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The optimal pebbling number of G is the smallest number of…

We study a recently introduced class of strategic games that is motivated by and generalizes Schelling's well-known residential segregation model. These games are played on undirected graphs, with the set of agents partitioned into multiple…