(0.001 seconds)

## 7 matching pages

##### 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, then ${\left(j,k\right)}$ is a product of $2k-2j-1$ adjacent transpositions: …Every permutation is a product of adjacent transpositions. Given a permutation $\sigma\in\mathfrak{S}_{n}$, the inversion number of $\sigma$, denoted $\mathop{\mathrm{inv}}(\sigma)$, is the least number of adjacent transpositions required to represent $\sigma$. …
##### 2: 34.7 Basic Properties: $\mathit{9j}$ Symbol
The $\mathit{9j}$ symbol has symmetry properties with respect to permutation of columns, permutation of rows, and transposition of rows and columns; these relate 72 independent $\mathit{9j}$ symbols. Even (cyclic) permutations of either columns or rows, as well as transpositions, leave the $\mathit{9j}$ 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, $\beta_{0}=\beta_{1}=0$, 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 $\mathbf{A}_{P}$ 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.