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 , 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 $\sigma \in {𝔖}_n$, 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

… ►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. …

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 ${𝐀}_P$ that lie below the main diagonal and its two adjacent diagonals. …

7: Bibliography S

… ►

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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External Links:

ISSN 0025-5718, Document, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.74(vi).

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