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Some examples of basic tools in Illustrator are selection tools, paintbrush tools, pen tools, pencil tools e.g. Selection tools are used to the layout, adjust, and organize the artwork by selecting, positioning, and stacking objects accurately. Moreover, selection tools can group, lock or hide, and measure objects. [24]
In geometric group theory, a graph of groups is an object consisting of a collection of groups indexed by the vertices and edges of a graph, together with a family of monomorphisms of the edge groups into the vertex groups. There is a unique group, called the fundamental group, canonically associated to each finite connected graph of groups. It ...
An illustrator is an artist who specializes in enhancing writing or concepts by providing a visual representation that corresponds to the content of the associated text or idea. The illustration may be intended to clarify complicated concepts or objects that are difficult to describe textually, which is the reason illustrations are often found ...
In terms of partition, 20 / 5 means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is ...
A normal form for a group G with generating set S is a choice of one reduced word in S for each element of G. For example: The words 1, i, j, ij are a normal form for the Klein four-group with S = {i, j} and 1 representing the empty word (the identity element for the group).
For instance, optimizing the cut size for free group sizes puts all vertices in the same community. Additionally, cut size may be the wrong thing to minimize since a good division is not just one with small number of edges between communities. This motivated the use of Modularity (Q) [13] as a metric to optimize a balanced graph partition.
However, there are three distinct ways of partitioning a square into three similar rectangles: [1] [2] The trivial solution given by three congruent rectangles with aspect ratio 3:1. The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ...
The subset of edges that have one endpoint in each side is called a cut-set. When a cut-set forms a complete bipartite graph, its cut is called a split. Thus, a split can be described as a partition of the vertices of the graph into two subsets X and Y, such that every neighbor of X in Y is adjacent to every neighbor of Y in X. [2]