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An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...
As Atneosen already observed, if edges may instead pass from one page to another across the spine of the book, then every graph may be embedded into a three-page book. [ 15 ] [ 2 ] [ 16 ] For such a three-page topological book embedding in which spine crossings are allowed, every graph can be embedded with at most a logarithmic number of spine ...
One may compute the linking number of each disjoint pair of curves formed in this way; if all pairs of cycles have zero linking number, the embedding is said to be linkless. [ 6 ] In some cases, a graph may be embedded in space in such a way that, for each cycle in the graph, one can find a disk bounded by that cycle that does not cross any ...
In mathematics, an embedding (or imbedding [1]) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X {\displaystyle X} is said to be embedded in another object Y {\displaystyle Y} , the embedding is given by some injective and structure-preserving map f : X → ...
On the other hand, it might well be that two (necessarily infinite) posets are mutually order-embeddable into each other without being order-isomorphic. An example is provided by the open interval ( 0 , 1 ) {\displaystyle (0,1)} of real numbers and the corresponding closed interval [ 0 , 1 ] {\displaystyle [0,1]} .
An embedded system on a plug-in card with processor, memory, power supply, and external interfaces. An embedded system is a specialized computer system—a combination of a computer processor, computer memory, and input/output peripheral devices—that has a dedicated function within a larger mechanical or electronic system.
Having a character have a dream is a common device to embed one narrative or scene within another. (Painting by William Blake, 1805) A story within a story, also referred to as an embedded narrative, is a literary device in which a character within a story becomes the narrator of a second story (within the first one). [1]
In this setting, one proves that every element of the group sufficiently close to the identity is the exponential of an element of the Lie algebra. [8] (The proof is practically identical to the proof of the closed subgroup theorem presented below.) It follows every closed subgroup is an embedded submanifold of GL(n, C) [16]