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Rule Of Division (combinatorics)
In combinatorics, the rule of division is a counting principle. It states that there are ways to do a task if it can be done using a procedure that can be carried out in ways, and for each way , exactly of the ways correspond to the way . In a nutshell, the division rule is a common way to ignore "unimportant" differences when counting things. Applied to Sets In the terms of a set: "If the finite set is the union of n pairwise disjoint subsets each with elements, then ." As a function The rule of division formulated in terms of functions: "If is a function from to where and are finite sets, and that for every value there are exactly values such that (in which case, we say that is -to-one), then ." Examples ''Example 1'' - How many different ways are there to seat four people around a circular table, where two seatings are considered the same when each person has the same left neighbor and the same right neighbor? :To solve this exercise we must first ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Round Table Rule Of Division
Round or rounds may refer to: Mathematics and science * Having no sharp corners, as an ellipse, circle, or sphere * Rounding, reducing the number of significant figures in a number * Round number, ending with one or more zeroes * Round (cryptography) * Roundness (geology) * Roundedness, when pronouncing vowels * Labialization, when pronouncing consonants Music * Round (music), a type of composition * ''Rounds'' (album), by Four Tet Places * The Round, a theatre in England * Round Point, in the South Shetland Islands * Rounds Mountain, in the US * Round Mountain (other), several places * Round Valley (other), several places Repeated activities * Round (boxing) * Round (dominoes) * Grand rounds, in medicine * Round of drinks * Funding round * Doing the rounds, or patrol Other uses * Round (surname) * Rounds (surname) * Round shot * Cartridge (firearms) * Round steak * Cattle * Bullion coins that are not legal tender, e.g. silver rounds * Rounds (webs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Principles
In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for Enumerative combinatorics, enumerative purposes. Bijective proofs are utilized to demonstrate that two sets have the same cardinality, number of elements. The pigeonhole principle often ascertains the existence of something or is used to determine the minimum or maximum number of something in a Discrete mathematics, discrete context. Many combinatorial identities arise from Double counting (proof technique), double counting methods or the method of distinguished element. Generating functions and recurrence relations are powerful tools that can be used to manipulate sequences, and can describe if not resolve many combinatorial situations. Rule of sum The rule of sum is an intuitive principle stating that if there are ''a'' possible outcomes for an event (or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
