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In 1912 Dehn gave an algorithm that solves both the word and conjugacy problem for the fundamental groups of closed orientable two-dimensional manifolds of genus greater than or equal to 2 (the genus 0 and genus 1 cases being trivial). It is known that the conjugacy problem is undecidable for many classes of groups. Classes of group ...
For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2] Words play an important role in the theory of free groups and presentations, and are central objects of study in ...
The third word is something everyone uses every day. Everyone knows what the third word means. What is the third word? [3] [21] The answer is "energy". The riddle says that the word ends in the letters g-r-y; it says nothing about the order of the letters. Many words end with "-rgy", but energy is something everyone uses every day.
Perfect rhyme (also called full rhyme, exact rhyme, [1] or true rhyme) is a form of rhyme between two words or phrases, satisfying the following conditions: [2] [3] The stressed vowel sound in both words must be identical, as well as any subsequent sounds. For example, the words kit and bit form a perfect rhyme, as do spaghetti and already in ...
Robot in a wooden maze. A maze-solving algorithm is an automated method for solving a maze.The random mouse, wall follower, Pledge, and Trémaux's algorithms are designed to be used inside the maze by a traveler with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that can see the whole maze at once.
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 ...
Other alphabets only use a subset of the Latin alphabet, such as Hawaiian and Italian, which uses the letters j, k, x, y, and w only in foreign words. [38] Another notable script is Elder Futhark, believed to have evolved out of one of the Old Italic alphabets. Elder Futhark gave rise to other alphabets known collectively as the Runic alphabets ...
When an answer is composed of multiple or hyphenated words, some crosswords (especially in Britain) indicate the structure of the answer. For example, "(3,5)" after a clue indicates that the answer is composed of a three-letter word followed by a five-letter word. Most American-style crosswords do not provide this information.
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