Roughly speaking, the family of combinatorial games consists of two-player games with
perfect information (no hidden information as in some card games), no chance moves (no …

A block graph is a graph in which every block is a complete graph. Let be a block graph and
let be the adjacency matrix of. We first obtain a formula for the determinant of over reals. It is …

Lie groups, and therefore Lie algebras, are fundamental structures in quantum physics that
determine the space of possible trajectories of evolving systems. However, classification and …

Consider an arbitrary field $ K $ and a finite-dimensional vector space $ X $ over $ K $
equipped with a, possibly degenerate, symplectic form $\omega $. Given a spanning subset …

This survey deals with pluri-periodic harmonic functions on lattices with values in a field of
positive characteristic. We mention, as a motivation, the game “Lights Out” following the work …

Roughly speaking, the family of combinatorial games consists of two-player games with
perfect information (no hidden information as in some card games), no chance moves (no …

A configuration of a graph is an assignment of one of two states, ON or OFF, to each vertex
of it. A regular move at a vertex changes the states of the neighbors of that vertex. A valid …

Let G be a graph in which each vertex can be in one of two states: on or off. In the σ-game,
when you “push” a vertex v you change the state of all of its neighbors, while in the σ+-game …

Let X=(V, E) be a finite simple connected graph with n vertices and m edges. A configuration
is an assignment of one of the two colors, black or white, to each edge of X. A move applied …

The paper deals with σ-games on grid graphs (in dimension 2 and more) and conditions
under which any completely symmetric configuration of lit vertices can be reached–in …