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adjacent transposition

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1: 26.13 Permutations: Cycle Notation
An adjacent transposition is a transposition of two consecutive integers. … Every transposition is the product of adjacent transpositions. If j < k , then ( j , k ) is a product of 2 k 2 j 1 adjacent transpositions: …Every permutation is a product of adjacent transpositions. Given a permutation σ 𝔖 n , the inversion number of σ , denoted inv ( σ ) , is the least number of adjacent transpositions required to represent σ . …
2: 34.7 Basic Properties: 9 j Symbol
The 9 j symbol has symmetry properties with respect to permutation of columns, permutation of rows, and transposition of rows and columns; these relate 72 independent 9 j symbols. Even (cyclic) permutations of either columns or rows, as well as transpositions, leave the 9 j symbol unchanged. …
3: 26.15 Permutations: Matrix Notation
The problème des ménages asks for the number of ways of seating n married couples around a circular table with labeled seats so that no men are adjacent, no women are adjacent, and no husband and wife are adjacent. …
4: 26.14 Permutations: Order Notation
A descent of a permutation is a pair of adjacent elements for which the first is larger than the second. …
5: 3.2 Linear Algebra
Tridiagonal matrices are ones in which the only nonzero elements occur on the main diagonal and two adjacent diagonals. …
6: 3.7 Ordinary Differential Equations
If, for example, β 0 = β 1 = 0 , then on moving the contributions of w ( z 0 ) and w ( z P ) to the right-hand side of (3.7.13) the resulting system of equations is not tridiagonal, but can readily be made tridiagonal by annihilating the elements of 𝐀 P that lie below the main diagonal and its two adjacent diagonals. …
7: Bibliography S
  • J. Segura (2001) Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros. Math. Comp. 70 (235), pp. 1205–1220.