combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set {1, 2, 3, ..., n} is a permutation (arrangement) of those numbers...

or signum of a permutation σ is denoted sgn(σ) and defined as +1 if σ is even and −1 if σ is odd. The signature defines the alternating character of the...

an alternating group is the group of even permutations of a finite set. The alternating group on a set of n elements is called the alternating group...

square to zero Alternating form, a function formula in algebra Alternating group, the group of even permutations of a finite set Alternating knot, a knot...

the permutation symbol, antisymmetric symbol, or alternating symbol, which refer to its antisymmetric property and definition in terms of permutations. The...

Unique Permutation Hashing. Mathematics portal Alternating permutation Convolution Cyclic order Even and odd permutations Josephus permutation Levi-Civita...

mathematical permutations. Alternating permutation Circular shift Cyclic permutation Derangement Even and odd permutations—see Parity of a permutation Josephus...

called alternate permutations, since the symbols in the original permutation alternate between odd and even integers. However, not all alternate permutations...

mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G...

entries 0.: 26  An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM...

alternating permutations of odd size are enumerated by the Euler numbers of odd index (also called tangent numbers) and the alternating permutations of...

in the former context. A permutation matrix is an alternating sign matrix, and an alternating sign matrix is a permutation matrix if and only if no entry...

kernel of this homomorphism, that is, the set of all even permutations, is called the alternating group An. It is a normal subgroup of Sn, and for n ≥ 2...

examples of fences. A linear extension of a fence is called an alternating permutation; André's problem of counting the number of different linear extensions...

the key as inputs, and applies several alternating rounds or layers of substitution boxes (S-boxes) and permutation boxes (P-boxes) to produce the ciphertext...

of online alternating selections appropriately centered and scaled converges to a normal distribution. Alternating permutation Permutation pattern and...

also alternating. In fact, this map is the "most general" alternating operator defined on V k ; {\displaystyle V^{k};} given any other alternating operator...

representation or alternating character, which takes a permutation to the one by one matrix with entry ±1 based on the sign of the permutation. These are the...

nontotient, noncototient, number of integer partitions of 20 with an alternating permutation. The HTTP 404 status code is usually sent from a web page if a...

lattice with the group of alternating bilinear forms on a lattice. Alternating algebra Bilinear map Exterior algebra § Alternating multilinear forms Map (mathematics)...

In mathematical analysis, the alternating series test proves that an alternating series is convergent when its terms decrease monotonically in absolute...

it is an alternating polynomial, not a symmetric polynomial. The defining property of the Vandermonde polynomial is that it is alternating in the entries...

In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action...

its action on pairs of elements of S is a rank 3 permutation group. In particular most of the alternating groups, symmetric groups, and Mathieu groups have...

occur in combinatorics, specifically when counting the number of alternating permutations of a set with an even number of elements. The odd-indexed Euler...

Zaghawa language, ISO 639-3 code Zag numbers, a type of alternating permutation Zag Industries, acquired by Stanley Black & Decker in 1990 Zags...

F. Trotter that generates all of the permutations of n {\displaystyle n} elements. Each two adjacent permutations in the resulting sequence differ by swapping...

trigonometric functions as generating functions in combinatorics, see Alternating permutation. Dirichlet kernel Euler's formula Exact trigonometric values Exponential...

The statistics of random permutations, such as the cycle structure of a random permutation are of fundamental importance in the analysis of algorithms...

the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of n {\displaystyle...