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23 relations: Bijection, Circular permutation in proteins, Conjugacy class, Coxeter group, Cycle index, Cycle sort, Cycles and fixed points, Disjoint sets, Function composition, Generating set of a group, Group (mathematics), Group action, Group theory, Mathematics, Multiset, Parity of a permutation, Permutation, Set (mathematics), Subset, Symmetric group, Transposable integer, Tuple, Well-defined.
Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Circular permutation in proteins
A circular permutation is a relationship between proteins whereby the proteins have a changed order of amino acids in their peptide sequence.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Coxeter group
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).
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Cycle index
In combinatorial mathematics a cycle index is a polynomial in several variables which is structured in such a way that information about how a group of permutations acts on a set can be simply read off from the coefficients and exponents.
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Cycle sort
Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm.
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Cycles and fixed points
In mathematics, the cycles of a permutation π of a finite set S correspond bijectively to the orbits of the subgroup generated by π acting on S. These orbits are subsets of S that can be written as, such that The corresponding cycle of π is written as (c1 c2... cn); this expression is not unique since c1 can be chosen to be any element of the orbit.
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Disjoint sets
In mathematics, two sets are said to be disjoint sets if they have no element in common.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Generating set of a group
In abstract algebra, a generating set of a group is a subset such that every element of the group can be expressed as the combination (under the group operation) of finitely many elements of the subset and their inverses.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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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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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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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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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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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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Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
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Transposable integer
The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are.
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Tuple
In mathematics, a tuple is a finite ordered list (sequence) of elements.
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Well-defined
In mathematics, an expression is called well-defined or unambiguous if its definition assigns it a unique interpretation or value.
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Adjacent transposition, Anticyclic permutation, Circular Permutation, Circular permutation, Transposition (mathematics).
References
[1] https://en.wikipedia.org/wiki/Cyclic_permutation
