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The permutation graph and the matching diagram for the permutation (4,3,5,1,2). In the mathematical field of graph theory, 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.
Interval graphs are exactly the graphs that are chordal and that have comparability graph complements. [7] A permutation graph is a containment graph on a set of intervals. [8] Therefore, permutation graphs are another subclass of comparability graphs. The trivially perfect graphs are the comparability graphs of rooted trees. [9]
In terms of permutations the two group elements of G / A 3 are the set of even permutations and the set of odd permutations. If the original group is that generated by a 120°-rotation of a plane about a point, and reflection with respect to a line through that point, then the quotient group has the two elements which can be described as the ...
The identity is its minimum, and the permutation formed by reversing the identity is its maximum. If a permutation were assigned to each inversion set using the element-based definition, the resulting order of permutations would be that of a Cayley graph, where an edge corresponds to the swapping of two elements on consecutive places. This ...
The Hamiltonian cycle in the Cayley graph of the symmetric group generated by the Steinhaus–Johnson–Trotter algorithm Wheel diagram of all permutations of length = generated by the Steinhaus-Johnson-Trotter algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red).
A map of the 24 permutations and the 23 swaps used in Heap's algorithm permuting the four letters A (amber), B (blue), C (cyan) and D (dark red) Wheel diagram of all permutations of length = generated by Heap's algorithm, where each permutation is color-coded (1=blue, 2=green, 3=yellow, 4=red).
In representation theory, the Ferrers diagrams correspond to the irreducible representations of the symmetric group of permutations, and the Young tableaux with a given shape form a basis of the irreducible representation with that shape. Therefore, the telephone numbers give the sum of the degrees of the irreducible representations.
Young diagram of shape (5, 4, 1), English notation Young diagram of shape (5, 4, 1), French notation. A Young diagram (also called a Ferrers diagram, particularly when represented using dots) is a finite collection of boxes, or cells, arranged in left-justified rows, with the row lengths in non-increasing order.