Related papers: New problems on old solitaire boards
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.
We give some new relations for Newman digit sums respectively different modulos and put some problems. In particular, for the odd prime modulos we put an important conjecture.
Classical billiards constitute an important class of dynamical systems. They have not only been in used in mathematical disciplines such as ergodic theory, but their properties demonstrate fundamental physical phenomena that can be observed…
We give a number of constructions where inverse limits seriously degrade properties of regular rings, such as unit-regularity, diagonalisation of matrices, and finite stable rank. This raises the possibility of using inverse limits to…
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
withdrawn Several symmetry problems are discussed. These include the Pompeiu problem and similar conjectures for the heat and wave equations.
Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical advice which was adopted by the manufacturer.…
In the game of Scrabble, letter tiles are drawn uniformly at random from a bag. The variability of possible draws as the game progresses is a source of variation that makes it more likely for an inferior player to win a head-to-head match…
Bridge is a trick-taking card game requiring the ability to evaluate probabilities since it is a game of incomplete information where each player only sees its cards. In order to choose a strategy, a player needs to gather information about…
The author has long enjoyed using the CSP refinement checker FDR to solve puzzles, as witnessed by examples in \cite{tpc,ucs}. Recent experiments have shown that a number of games of patience (card games for one) are now well within bounds.…
In this short note we briefly review some recent mathematical results relevant to the classical Regge Calculus evolution problem.
The New York Times (NYT) games have found widespread popularity in recent years and reportedly account for an increasing fraction of the newspaper's readership. In this paper, we bring the computational lens to the study of New York Times…
We discuss fun problems, vaguely related to notions and theorems of a course in differential geometry. This paper can be regarded as a weekend "treasure chest" supplementing the course weekday lecture notes. The problems and solutions are…
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the…
Several results about the union-closed sets conjecture are presented.
This paper describes problems with the current way we compare the diversity of different recommendation lists in offline experiments. We illustrate the problems with a case study. We propose the Sudden Death score as a new and better way of…
Planar drawings of graphs tend to be favored over non-planar drawings. Testing planarity and creating a planar layout of a planar graph can be done in linear time. However, creating readable drawings of nearly planar graphs remains a…
We consider some examples of superintegrable system which were recently isolated through a differential Galois group analysis. The identity of these systems is clarified and the corresponding Poisson algebras derived.