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A tree diagram may represent a series of independent events (such as a set of coin flips) or conditional probabilities (such as drawing cards from a deck, without replacing the cards). [1] Each node on the diagram represents an event and is associated with the probability of that event. The root node represents the certain event and therefore ...
Schematic illustration of a combinatorial species structure on five elements by using a Labelle diagram. Any species consists of individual combinatorial structures built on the elements of some finite set: for example, a combinatorial graph is a structure of edges among a given set of vertices, and the species of graphs includes all graphs on all finite sets.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
Syntax is usually associated with the rules (or grammar) governing the composition of texts in a formal language that constitute the well-formed formulas of a formal system. In computer science, the term syntax refers to the rules governing the composition of well-formed expressions in a programming language. As in mathematical logic, it is ...
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]
A logical graph is a special type of graph-theoretic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic.. In his papers on qualitative logic, entitative graphs, and existential graphs, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.
Tree topology, a topology based on a hierarchy of nodes in a computer network; Tree diagram (physics), an acyclic Feynman diagram, pictorial representations of the mathematical expressions governing the behavior of subatomic particles; Outliners, a common software application that is used to generate tree diagrams; Network diagram; Tree ...
The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ = 1 and t = 2 or (recently) t ≥ 2.