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The reason is that, in general, there are many different possible ways to draw a Hasse diagram for a given poset. The simple technique of just starting with the minimal elements of an order and then drawing greater elements incrementally often produces quite poor results: symmetries and internal structure of the order are easily lost.
A partial order of dimension 4 (shown as a Hasse diagram) and four total orderings that form a realizer for this partial order.. In mathematics, the dimension of a partially ordered set (poset) is the smallest number of total orders the intersection of which gives rise to the partial order.
A partially ordered set (poset for short) is an ordered pair = (,) consisting of a set (called the ground set of ) and a partial order on . When the meaning is clear from context and there is no ambiguity about the partial order, the set X {\displaystyle X} itself is sometimes called a poset.
A nontrivial poset satisfying the descending chain condition is said to have deviation 0. Then, inductively, a poset is said to have deviation at most α (for an ordinal α) if for every descending chain of elements a 0 > a 1 >... all but a finite number of the posets of elements between a n and a n+1 have deviation less than α. The deviation ...
Every cofinal subset of a partially ordered set with maximal elements must contain all maximal elements. A subset L {\displaystyle L} of a partially ordered set P {\displaystyle P} is said to be a lower set of P {\displaystyle P} if it is downward closed: if y ∈ L {\displaystyle y\in L} and x ≤ y {\displaystyle x\leq y} then x ∈ L ...
The Euler characteristic of such a poset is defined as the integer μ(0,1), where μ is the Möbius function in that poset's incidence algebra. This can be further generalized by defining a rational valued Euler characteristic for certain finite categories , a notion compatible with the Euler characteristics of graphs, orbifolds and posets ...
The process of geometric drawing is based on constructions with a ruler and compass, which in turn are based on the first three postulates of Euclid's Elements. The historical importance of rulers and compasses as instruments in solving geometric problems leads many authors to limit Geometric Drawing to the representation and solution of ...
A cutaway drawing is a technical illustration, in which part of the surface of a three-dimensional model is removed in order to show some of the model's interior in relation to its exterior. The purpose of a cutaway drawing is to "allow the viewer to have a look into an otherwise solid opaque object.