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Combinatorial Cube
In the mathematical study of combinatorics on words, a parameter word is a string over a given alphabet having some number of wildcard characters. The set of strings matching a given parameter word is called a parameter set or combinatorial cube. Parameter words can be composed, to produce smaller subcubes of a given combinatorial cube. They have applications in Ramsey theory and in computer science in the detection of duplicate code. Definitions and notation Formally, a word of length n, over a given alphabet A, is a sequence of n characters, some of which may be drawn from A and the others of which are k distinct wildcard characters *_1,*_2,\ldots, *_k. Each wildcard character is required to appear at least once, but may appear multiple times, and the wildcard characters must appear in the order given by their indexes: the first wildcard character in the word must be *_1, the next one that is different from *_1 must be *_2, etc. As a special case, a word over the given alphabet, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics On Words
Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words affects various areas of mathematical study, including algebra and computer science. There have been a wide range of contributions to the field. Some of the first work was on square-free words by Axel Thue in the early 1900s. He and colleagues observed patterns within words and tried to explain them. As time went on, combinatorics on words became useful in the study of algorithms and coding. It led to developments in abstract algebra and answering open questions. Definition Combinatorics is an area of discrete mathematics. Discrete mathematics is the study of countable structures. These objects have a definite beginning and end. The study of enumerable objects is the opposite of disciplines such as analysis, where calculus and in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
