Order Dimension - Formal Definition

Formal Definition

The dimension of a poset P is the least integer t for which there exists a family

of linear extensions of P so that, for every x and y in P, x precedes y in P if and only if it precedes y in each of the linear extensions. That is,

Read more about this topic:  Order Dimension

Other articles related to "formal definition":

Atomic SP-DEVS - Formal Definition
... The above controller for crosswalk lights can be modeled by an atomic SP-DEVS model ... Formally, an atomic SP-DEVS is a 7-tuple where is a finite set of input events is a finite set of output events is a finite set of states is the initial state is the time advanced function which defines the lifespan of a state where is the set of non-negative rational numbers plus infinity ...
Big O Notation - Example
... In typical usage, the formal definition of O notation is not used directly rather, the O notation for a function f(x) is derived by the following simplification ... One may confirm this calculation using the formal definition let f(x) = 6x4 − 2x3 + 5 and g(x) = x4 ... Applying the formal definition from above, the statement that f(x) = O(x4) is equivalent to its expansion, for some suitable choice of x0 and M and for all x > x0 ...

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