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Under this definition, an enumeration of a set S is any surjection from an ordinal α onto S. The more restrictive version of enumeration mentioned before is the special case where α is a finite ordinal or the first limit ordinal ω. This more generalized version extends the aforementioned definition to encompass transfinite listings.
In computer science, an enumeration algorithm is an algorithm that enumerates the answers to a computational problem. Formally, such an algorithm applies to problems that take an input and produce a list of solutions, similarly to function problems. For each input, the enumeration algorithm must produce the list of all solutions, without ...
An enumerated type is an ordinal type, and the pred and succ functions will give the prior or next value of the enumeration, and ord can convert enumeration values to their integer representation. Standard Pascal does not offer a conversion from arithmetic types to enumerations, however.
According to the Church–Turing thesis, any effectively calculable function is calculable by a Turing machine, and thus a set S is computably enumerable if and only if there is some algorithm which yields an enumeration of S. This cannot be taken as a formal definition, however, because the Church–Turing thesis is an informal conjecture ...
The problem of finding a closed formula is known as algebraic enumeration, and frequently involves deriving a recurrence relation or generating function and using this to arrive at the desired closed form. Often, a complicated closed formula yields little insight into the behavior of the counting function as the number of counted objects grows.
The complete list of all free trees on 2, 3, and 4 labeled vertices: = tree with 2 vertices, = trees with 3 vertices, and = trees with 4 vertices.. In combinatorics, an area of mathematics, graph enumeration describes a class of combinatorial enumeration problems in which one must count undirected or directed graphs of certain types, typically as a function of the number of vertices of the ...
An enumerator is a Turing machine equipped with an attached printer. the first sentence to avoid redundancy. Every time the Turing machine wants to add a string to the list, it sends the string to the printer.
Enumeration, a mathematical, theoretical concept of an exhaustive listing of compatible items; Enumerate (project), a collaborative research project about ...