dominations

Domination is the state or practice of one actor, group, or system exerting control or influence over others. The plural dominations is used to refer to multiple instances, forms, or case studies of domination across different domains.

In political science and sociology, domination describes asymmetric power relations within societies, institutions, and networks. Analyses examine how power is maintained through coercion, ideology, law, and economic structures, as well as how subordinate groups contest or resist domination through protest, organization, and reform movements. The concept often intersects with questions of legitimacy, inequality, and social change.

In mathematics, domination has several precise meanings. In graph theory, a dominating set D of a graph G is a subset of vertices such that every vertex not in D is adjacent to at least one vertex in D. The size of the smallest dominating set is the domination number gamma(G). In analysis, domination appears in the notion of dominating functions, which bound a family of functions to ensure convergence results such as the dominated convergence theorem and related inequalities.

In ecology, dominance refers to dominance hierarchies within animal groups, where individuals are ranked and higher-ranked members typically have priority access to resources such as food, mates, or space. Such hierarchies influence behavior, reproduction, and survival, and can be shaped by genetics, experience, and environmental conditions.

In economics and game theory, domination by a strategy or a firm can lead to the formulation of dominant strategies or market power, shaping competitive dynamics. Across disciplines, dominations highlight how power, influence, or resource access emerges, is maintained, and is challenged within complex systems.