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First and foremost, a word is basically a sequence of symbols, or letters, in a finite set. [1] One of these sets is known by the general public as the alphabet. For example, the word "encyclopedia" is a sequence of symbols in the English alphabet, a finite set of twenty-six letters. Since a word can be described as a sequence, other basic ...
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states: Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast.
The word problem was one of the first examples of an unsolvable problem to be found not in mathematical logic or the theory of algorithms, but in one of the central branches of classical mathematics, algebra. As a result of its unsolvability, several other problems in combinatorial group theory have been shown to be unsolvable as well.
Two of the problems are trivial (the number of equivalence classes is 0 or 1), five problems have an answer in terms of a multiplicative formula of n and x, and the remaining five problems have an answer in terms of combinatorial functions (Stirling numbers and the partition function for a given number of parts).
For functions in certain classes, the problem of determining: whether two functions are equal, known as the zero-equivalence problem (see Richardson's theorem); [4] the zeroes of a function; whether the indefinite integral of a function is also in the class. [5] Of course, some subclasses of these problems are decidable.
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.
Despite the case being dismissed in July, Alec Baldwin says the story surrounding the fatal “Rust” shooting has only begun. On the Dec. 16 episode of David Duchovny’s “Fail Better ...
If, for example, there are two balls and three bins, then the number of ways of placing the balls is (+) = =. The table shows the six possible ways of distributing the two balls, the strings of stars and bars that represent them (with stars indicating balls and bars separating bins from one another), and the subsets that correspond to the strings.
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