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 …

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 …

Each vertex in a simple graph is in one of two states:“on” or “off”. The set of all on vertices is
called a configuration. In the σ-game,“pushing” a vertex v changes the state of all vertices in …

Let Γ be a connected graph. For any x∈ F2V (Γ), a move of the lit-only sigma game on Γ
consists of choosing some v∈ V (Γ) with x (v)= 1 and changing the values of x at all those …

A configuration of the lit-only σ σ-game on a graph Γ Γ is an assignment of one of two states,
on or off, to each vertex of Γ Γ. Given a configuration, a move of the lit-only σ σ-game on Γ Γ …

Let $ W $ denote a simply-laced Coxeter group with $ n $ generators. We construct an $ n $-
dimensional representation $\phi $ of $ W $ over the finite field $ F_2 $ of two elements. The …

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 …

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 …