world order requires a huge number of different phenomena and objects.At the same time science proves that this abundance is based on a set of a certain number of components.Connecting in a different order, these blocks are the basis for the architectural constructions of the world around us.The study of the number of all possible variants of a combination of the various components involved in mathematics, in particular its section called combinatorics.
Thus, as objects of study takes discrete values of the set (permutations, combinations, transfer and placement of elements), and the ratio on them (optionally partial order).Elements of combinatorics have a close relationship with geometry and algebra, they practically became the basis for the calculation of probability theory.A wide range of different fields of knowledge is impossible to imagine without the use of this field of science.The most popular branch of mathematics that began in statistical physics, genetics and computer science.
And the beginning of his term "combinatorics" takes from 1666.In his work "Discourse on the combinatorial art" mathematician Leibniz laid the foundation for further development of this branch of mathematics.
Very often, using the term "combinatorics", taking into account a much wider section of discrete mathematics, which includes, for example, the graph theory.
Elements of combinatorics is often presented as a model of combinatorial configurations.Accommodation, permutation, combination, composition and decomposition of the number are the main components, which embodied the principles of this branch of mathematics.
Placement - an ordered set of a certain number of components belonging to a set, with a well-defined number of elements.Permutation is called a strictly ordered set of a fixed number of elements.Combinatorics combination - is taken from a set number of items included in the data.Sets have differences only in the order of the elements, but the composition is the same, this is the difference between the combination and placement.The number of combinations of a set depends on the size and number of elements that make up the set of numbers that are taken to produce the said combinatorial model.
Considering the composition of the concept, take it all as a representation of the amount ordered from the positive integers.But the partition of - is it any idea of how disordered the sum of positive integers.
elements of combinatorics are widely used in various fields of knowledge.At the same time she does this as part of mathematics took a dramatic development that has enabled the accumulated baggage information in this field to allocate partitions.
Considering discipline of a section entitled "Combinatorial enumeration" (quantifiable), taking into account the transfer or counting the number of possible configurations (for example, permutations), which are formed from the elements of finite sets.It is possible the imposition of certain restrictions.These include invisibility or apparent elements permit repetition of the same elements, and so forth.
to count the number of configurations that use the classical rules of addition and multiplication.Elements of combinatorics in this section apply discipline to solve a wide spectrum of various tasks.
in structural combinatorics add a number of problems in the theory of graphs, shows the influence of the theory of matroids.Among the sections of the discipline it stands out as an extreme combinatorics, Ramsey theory, probability, topology, combinatorics infinitary.
