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2. Combinatorics on words - Wikipedia

   en.wikipedia.org/wiki/Combinatorics_on_words

   First and foremost, a word is basically a sequence of symbols, or letters, in a finite set. [1] One of these sets is known by the general public as the alphabet. For example, the word "encyclopedia" is a sequence of symbols in the English alphabet, a finite set of twenty-six letters. Since a word can be described as a sequence, other basic ...

3. Word problem for groups - Wikipedia

   en.wikipedia.org/wiki/Word_problem_for_groups

   The word problem is a well-known example of an undecidable problem. If A {\displaystyle A} is a finite set of generators for G {\displaystyle G} , then the word problem is the membership problem for the formal language of all words in A {\displaystyle A} and a formal set of inverses that map to the identity under the natural map from the free ...

4. Word problem (mathematics education) - Wikipedia

   en.wikipedia.org/wiki/Word_problem_(mathematics...

   Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

5. Word problem (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Word_problem_(mathematics)

   The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]

6. Word (group theory) - Wikipedia

   en.wikipedia.org/wiki/Word_(group_theory)

   In group theory, a word is any written product of group elements and their inverses. 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 }.

7. Combinatorics - Wikipedia

   en.wikipedia.org/wiki/Combinatorics

   Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures.It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.