Related papers: A Gale-Berlekamp permutation-switching problem in …
Given a graph G and integers b and w. The black-and-white coloring problem asks if there exist disjoint sets of vertices B and W with |B|=b and |W|=w such that no vertex in B is adjacent to any vertex in W. In this paper we show that the…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
We consider the problem of finding the set of permutations $r_j$ of $\{1,\cdots , n\}$ such that $\sum_{i=1}^n \prod_{j=1}^k r_j(i)$ is maximized or minimized. While the set of permutations maximizing this value are easily determined,…
The Bandwidth Problem seeks for a simultaneous permutation of the rows and columns of the adjacency matrix of a graph such that all nonzero entries are as close as possible to the main diagonal. This work focuses on investigating novel…
The main problem addressed here is to decide whether it is possible or not to go from a given position on a peg-solitaire board to another one. No non-trivial sufficient conditions are known, but tests have been devised to show…
We are given $n$ balls and an unknown coloring of them with two colors. Our goal is to find a ball that belongs to the larger color class, or show that the color classes have the same size. We can ask sets of $k$ balls as queries, and the…
We introduce a game on graphs. By a theorem of Zermelo, each instance of the game on a finite graph is determined. While the general decision problem on which player has a winning strategy in a given instance of the game is unsolved, we…
Neighborhood Lights Out is a game played on graphs. Begin with a graph and a vertex labeling of the graph from the set $\{0,1,2,\dots, \ell-1\}$ for $\ell \in \mathbb{N}$. The game is played by toggling vertices: when a vertex is toggled,…
The list coloring problem is a variation of the classical vertex coloring problem, extensively studied in recent years, where each vertex has a restricted list of allowed colors, and having some variations as the $(\gamma,\mu)$-coloring,…
We define a variant of the two-dimensional Silver Dollar game. Two coins are placed on a chessboard of unbounded size, and two players take turns choosing one of the coins and moving it. Coins are to be moved to the left or upward…
We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…
In this work a lattice formulation of a supersymmetric theory is proposed and tested that preserves the complete supersymmetry on the lattice. The results of a one-dimensional nonperturbative simulation show the realization of the full…
We consider a general five-dimensional sigma-model coupled to gravity, with any number of scalars and general sigma-model metric and potential. We discuss in detail the problem of the boundary conditions for the scalar fluctuations, in the…
The Bell inequalities in three and four correlations are re-derived in general forms showing that three and four data sets, respectively, identically satisfy them regardless of whether they are random, deterministic, measured, predicted, or…
In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, for an optimal control, we build up an upper bound for the number of its switching points; show that…
An alternating colouring function is defined on strings over the alphabet $\{0, 1\}$. It divides the strings in colourable and non-colourable ones. The points in the subshift of finite type defined by forbidding all non-colourable strings…
This paper studies the time optimal control problem for systems of heat equations coupled by a pair of constant matrices. The control constraint is of the ball-type, while the target is the origin of the state space. We obtain an upper…
A permutation of size $n$ can be identified to its diagram in which there is exactly one point per row and column in the grid $[n]^2$. In this paper we consider multidimensional permutations (or $d$-permutations), which are identified to…
Seidel's switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non-adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching-equivalent if one…
We provide a criterion for determining the winner in two-player win-lose alternating-move games on trees, in terms of the Hausdorff dimension of the target set. We focus our study on special cases, including the Gale-Stewart game on the…