# adjacent transposition

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## 7 matching pages

##### 1: 26.13 Permutations: Cycle Notation

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►An

*adjacent transposition*is a transposition of two consecutive integers. … ►Every transposition is the product of adjacent transpositions. If $$, 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 $\sigma \in {\U0001d516}_{n}$, the*inversion number*of $\sigma $, denoted $inv(\sigma )$, is the least number of adjacent transpositions required to represent $\sigma $. …##### 2: 34.7 Basic Properties: $\mathit{9}j$ Symbol

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►The $\mathit{9}j$ symbol has symmetry properties with respect to permutation of columns, permutation of rows, and transposition of rows and columns; these relate 72 independent $\mathit{9}j$ symbols.
Even (cyclic) permutations of either columns or rows, as well as transpositions, leave the $\mathit{9}j$ symbol unchanged.
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##### 3: 26.15 Permutations: Matrix Notation

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*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

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*descent*of a permutation is a pair of adjacent elements for which the first is larger than the second. …##### 5: 3.2 Linear Algebra

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*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

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►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.
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##### 7: Bibliography S

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Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros.
Math. Comp. 70 (235), pp. 1205–1220.
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