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Inversion (discrete mathematics)

Index Inversion (discrete mathematics)

In computer science and discrete mathematics a sequence has an inversion where two of its elements are out of their natural order. [1]

25 relations: Cayley graph, Comparison sort, Computer science, Damerau–Levenshtein distance, Discrete mathematics, Factorial number system, Introduction to Algorithms, Journal of Graph Algorithms and Applications, Kendall tau distance, Lattice (order), Lehmer code, Lexicographical order, Multiset, N-skeleton, On-Line Encyclopedia of Integer Sequences, Parity of a permutation, Partially ordered set, Permutation, Permutation graph, Permutohedron, Sequence, Subset, The Art of Computer Programming, Total order, Wolfram Mathematica.

Cayley graph

In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group.

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Comparison sort

A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Damerau–Levenshtein distance

In information theory and computer science, the Damerau–Levenshtein distance (named after Frederick J. Damerau and Vladimir I. Levenshtein.) is a string metric for measuring the edit distance between two sequences.

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Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

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Factorial number system

In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations.

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Introduction to Algorithms

Introduction to Algorithms is a book by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.

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Journal of Graph Algorithms and Applications

The Journal of Graph Algorithms and Applications is an open access peer-reviewed scientific journal covering the subject of graph algorithms and graph drawing.

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Kendall tau distance

The Kendall tau rank distance is a metric that counts the number of pairwise disagreements between two ranking lists.

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Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

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Lehmer code

In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers.

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Lexicographical order

In mathematics, the lexicographic or lexicographical order (also known as lexical order, dictionary order, alphabetical order or lexicographic(al) product) is a generalization of the way words are alphabetically ordered based on the alphabetical order of their component letters.

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Multiset

In mathematics, a multiset (aka bag or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements.

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N-skeleton

In mathematics, particularly in algebraic topology, the of a topological space X presented as a simplicial complex (resp. CW complex) refers to the subspace Xn that is the union of the simplices of X (resp. cells of X) of dimensions In other words, given an inductive definition of a complex, the is obtained by stopping at the.

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On-Line Encyclopedia of Integer Sequences

The On-Line Encyclopedia of Integer Sequences (OEIS), also cited simply as Sloane's, is an online database of integer sequences.

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Parity of a permutation

In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations.

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Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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Permutation graph

In mathematics, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs of elements that are reversed by the permutation.

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Permutohedron

In mathematics, the permutohedron of order n (also spelled permutahedron) is an (n − 1)-dimensional polytope embedded in an n-dimensional space, the vertices of which are formed by permuting the coordinates of the vector (1, 2, 3,..., n).

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Sequence

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.

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Subset

In mathematics, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide.

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The Art of Computer Programming

The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.

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Total order

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set X, which is antisymmetric, transitive, and a connex relation.

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Wolfram Mathematica

Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.

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Inversion (combinatorics), Inversion (computer science), Inversion number, Inversion vector, Weak order of permutations.

References

[1] https://en.wikipedia.org/wiki/Inversion_(discrete_mathematics)

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