size: the even permutations and the odd permutations. If any total ordering of X is fixed, the parity (oddness or evenness) of a permutation σ {\displaystyle...

whether a number is even or odd Parity of a permutation, indicates whether a permutation has an even or odd number of inversions Parity function, a Boolean...

a permutation of a set can mean one of two different things: an arrangement of its members in a sequence or linear order, or the act or process of changing...

found. The parity of a permutation (as defined in abstract algebra) is the parity of the number of transpositions into which the permutation can be decomposed...

theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation...

specified for use as parity bits. This permutation selects the 48-bit subkey for each round from the 56-bit key-schedule state. This permutation will ignore 8...

odd permutations—see Parity of a permutation Josephus permutation Parity of a permutation Separable permutation Stirling permutation Superpattern Transposition...

_{1\,2\,\dots n},} where p (called the parity of the permutation) is the number of pairwise interchanges of indices necessary to unscramble i1, i2, ...

potentially lead to a secure implementation. The permutation parity machine is a binary variant of the tree parity machine. It consists of one input layer...

the contents of cubicle 1 is swapped with the contents of cubicle 2, etc. The parity of a permutation refers to whether that permutation is even or odd...

inversion in a sequence is a pair of elements that are out of their natural order. Let π {\displaystyle \pi } be a permutation. There is an inversion of π {\displaystyle...

invariant is the parity of the permutation of all 16 squares plus the parity of the taxicab distance (number of rows plus number of columns) of the empty square...

A) // Generate permutations for k-th swapped with each k-1 initial for i := 0; i < k-1; i += 1 do // Swap choice dependent on parity of k (even or odd)...

short proofs of the invariance of this parity of a permutation. The product of two even permutations is even, the product of two odd permutations is even,...

of a given colour. This is raised to the sixth power because there are six colours. An odd permutation of the corners implies an odd permutation of the...

character sgn {\displaystyle \operatorname {sgn} } , of Sn, defined by the parity of a permutation. The permanent is the case where χ λ {\displaystyle...

other words, its parity—the quality of an integer being even or odd—is even. This can be easily verified based on the definition of "even": it is an integer...

volume of the parallelepiped, it is the signed volume, the sign depending on the orientation of the frame or the parity of the permutation of the vectors...

{1}{2}}\end{bmatrix}}} With permutation matrices the determinant matches the signature, being +1 or −1 as the parity of the permutation is even or odd, for the...

pieces of a given color. This is raised to the sixth power because there are six colors. The total number of center permutations is the permutations of a single...

from the parity of the permutation. Multiplying these together yields a third map C n → { ± 1 } {\displaystyle C_{n}\to \{\pm 1\}} . The kernel of the first...

uncorrected errors. By contrast, the simple parity code cannot correct errors, and can detect only an odd number of bits in error. Hamming codes are perfect...

S_{n}}(-1)^{\sigma }a_{1\sigma (1)}\cdots a_{n\sigma (n)},} where Sn is the group of all permutations of n elements, σ is a permutation, and (−1)σ the parity of the permutation...

indicate the type of reply. The final 24 bits in each case is combined aircraft address and parity. Eleven permutations have been allocated. A transponder equipped...

sequence and its permutation. The complement of a permutation graph is another permutation graph, for the reverse of the given permutation. Therefore, as...

12!/2 × 211 or 12! × 210 possibilities (an odd permutation of the corners implies an odd permutation of the central edges, and vice versa, thus the division...

pieces of a given color. This is raised to the sixth power because there are six colors. The total number of center permutations is the permutations of a single...

either a permutation is always decomposed in an even number of transpositions (the permutation is called even and has the parity +1), or a permutation is...

positions of eight pieces in two, odd parity, four cycles. Overall, a face turn is an even permutation. On the regular cube a 90˚ rotation of the whole...

particle physics, CP violation is a violation of CP-symmetry (or charge conjugation parity symmetry): the combination of C-symmetry (charge conjugation symmetry)...