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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 ...
In the mathematical study of combinatorics on words, a parameter word is a string over a given alphabet having some number of wildcard characters. [1] 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.
The theorem can be used in analytic combinatorics to estimate the number of words of length n generated by a given unambiguous context-free grammar, as n grows large. The following example is given by Gruber, Lee & Shallit (2012): the unambiguous context-free grammar G over the alphabet {0,1} has start symbol S and the following rules
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This can be proved by constructing a square-free word without the two-letter combination ab. As a result, bcba cbca cbaca is the longest square-free word without the combination ab and its length is equal to 13. Note that over a more than three-letter alphabet there are square-free words of any length without an arbitrary two-letter combination.
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Word ladder (also known as Doublets, [1] word-links, change-the-word puzzles, paragrams, laddergrams, [2] or word golf) is a word game invented by Lewis Carroll. A word ladder puzzle begins with two words, and to solve the puzzle one must find a chain of other words to link the two, in which two adjacent words (that is, words in successive ...