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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) - 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]

5. Combination - Wikipedia

   en.wikipedia.org/wiki/Combination

   In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.

6. Kirkman's schoolgirl problem - Wikipedia

   en.wikipedia.org/wiki/Kirkman's_schoolgirl_problem

   A solution to Kirkman's schoolgirl problem with vertices denoting girls and colours denoting days of the week [1] Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states:

7. List of NP-complete problems - Wikipedia

   en.wikipedia.org/wiki/List_of_NP-complete_problems

   The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23

8. 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.

9. Combinatorial explosion - Wikipedia

   en.wikipedia.org/wiki/Combinatorial_explosion

   Combinatorial explosion is sometimes used to justify the intractability of certain problems. [1] [2] Examples of such problems include certain mathematical functions, the analysis of some puzzles and games, and some pathological examples which can be modelled as the Ackermann function.