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In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression.The process of finding or using such a code is Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes".
The concept of an n-ary group can be further generalized to that of an (n,m)-group, also known as a vector valued group, which is a set G with a map f: G n → G m where n > m, subject to similar axioms as for an n-ary group except that the result of the map is a word consisting of m letters instead of a single letter.
n-ary may refer to: The arity of a function, operation, or relation n-ary associativity, a specific rule attached to n-ary functions n-ary group, a generalization of group; The radix of a numerical representation system; The number of letters in an alphabet (formal languages) An n-ary code. An n-ary Gray code; An n-ary Huffman code; An n-ary tree
In graph theory, an m-ary tree (for nonnegative integers m) (also known as n-ary, k-ary or k-way tree) is an arborescence (or, for some authors, an ordered tree) [1] [2] in which each node has no more than m children. A binary tree is an important case where m = 2; similarly, a ternary tree is one where m = 3.
The algorithms represent the dictionary as an n-ary tree where n is the number of tokens used to form token sequences. Each dictionary entry is of the form dictionary[...] = {index, token} , where index is the index to a dictionary entry representing a previously seen sequence, and token is the next token from the input that makes this entry ...
Choosing k = n, b 1 = ... = b n = 1 this implies that the entropy of a certain outcome is zero: Η 1 (1) = 0. This implies that the efficiency of a source set with n symbols can be defined simply as being equal to its n-ary entropy. See also Redundancy (information theory).
In mathematics, a finitary relation over a sequence of sets X 1, ..., X n is a subset of the Cartesian product X 1 × ... × X n; that is, it is a set of n-tuples (x 1, ..., x n), each being a sequence of elements x i in the corresponding X i. [1] [2] [3] Typically, the relation describes a possible connection between the elements of an n-tuple.
Defining an identity with respect to join makes it possible to extend the binary join operator into a n-ary join operator. [1]:89. Since the relational Cartesian product is a special case of join, the zero-degree relation of cardinality 1 is also the identity with respect to the Cartesian product. [1]:89
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