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Examples of the the word, permutation , in a Sentence Context

The word ( permutation ), is the 19712 most frequently used in English word vocabulary

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  1. Key K. M is termed the plaintext and C the ciphertext. For each key K, EK is a, permutation ,(a bijective mapping) over the set of input blocks. Each key selects one
  2. Also known as the symmetric group on n elements) is denoted Sn. For each, permutation ,σ, sgn (σ) denotes the signature of σ; it is +1 for even σ and −1 for odd σ.
  3. A bijective mapping) over the set of input blocks. Each key selects one, permutation ,from the possible set of (2^n)!. The block size, n,is typically 64 or 128
  4. Algorithms not generally available to interpreters (e.g., upgrade of, permutation ,vector),to achieve a level of performance comparable to that of FORTRAN. The
  5. Algorithm — the attacker can distinguish the cipher from a random, permutation , Similar considerations apply to attacks on other types of cryptographic
  6. Entries. The determinant of P is just the sign \var epsilon of the corresponding, permutation , The determinant of A is then: \DET (A) = \var epsilon \DET (L)\dot\DET (U
  7. Automorphism is a group isomorphism from a group to itself. Informally, it is a, permutation ,of the group elements such that the structure remains unchanged. For every
  8. Context. Examples * In set theory, an automorphism of a set X is an arbitrary, permutation ,of the elements of X. The automorphism group of X is also called the symmetric
  9. For even σ and −1 for odd σ. Evenness or oddness can be defined as follows: the, permutation ,is even (odd) if the new sequence can be obtained by an even number (odd
  10. Which examines only 5,508 possible queen placements is to combine the, permutation ,based method with the early pruning method: the permutation s are generated
  11. By considering the n! Permutations of all the elements of S. Each such, permutation ,gives a k-combination by selecting its first k elements. There are many
  12. Class onto itself, such bijections are also known as permutation s. Hence, permutation ,groups (also known as transformation groups) and the related notion of orbit
  13. Three (an odd number) switches,3,2,1 results. Therefore, 3,2,1 is an odd, permutation , Similarly, the permutation 2,3,1 is even (1,2,3 → 2,1,3 → 2,3,1,with
  14. Attacks for AES-like permutation s, which view two consecutive rounds of, permutation ,as the application of a so-called Super-Sbox. It works on the 8-round version
  15. Fixpoints have the same cardinality, corresponding to cycles of length one in a, permutation , Functions equivalent in this manner from an equivalence class on X→X, and
  16. Z2 × Z2). Since this group is Abelian, every subgroup is normal; but every, permutation ,of the three non-identity elements is an automorphism of V, so the three
  17. And projective map. A bijective function from a set to itself is also called a, permutation , Composition and inverses A function f: X \right arrow Y is bijective if and
  18. Of multilinear alternating maps). Iterating gives that more generally a, permutation ,of the columns multiplies the determinant by the sign of the permutation .
  19. 1 through 8 (of which there are 8! = 40,320),and uses the elements of each, permutation ,as indices to place a queen on each row. Then it rejects those boards with
  20. Innovator, Gysin altered the cut-up technique to produce what he called, permutation ,poems in which a single phrase was repeated several times with the words
  21. Usual plaintext or ciphertext input. The tweak, along with the key, selects the, permutation ,computed by the cipher. If changing tweaks is sufficiently lightweight (
  22. The Leibniz formula (or from the Laplace expansion),in which the identity, permutation ,is the only one that gives a non-zero contribution. These properties can be
  23. 1 is even (1,2,3 → 2,1,3 → 2,3,1,with an even number of switches). A, permutation ,cannot be simultaneously even and odd. In any of the n! Summands, the term:
  24. The recurrence relation:: =++\lots+ and symmetry:: = where (\sigma_i) is a, permutation ,of (1,2,..., r ). Generalization to negative integers If k \GEQ 0,then \franc
  25. Finally, the 32 outputs from the S-boxes are rearranged according to a fixed, permutation , the P-box. This is designed so that, after expansion, each S-box's output
  26. Columns multiplies the determinant by the sign of the permutation . Similarly, a, permutation ,of the rows multiplies the determinant by the sign of the permutation . #Adding
  27. The backtracking depth-first search program, a slight improvement on the, permutation ,method, constructs the search tree by considering one row of the board at a
  28. A permutation of the columns multiplies the determinant by the sign of the, permutation , Similarly, a permutation of the rows multiplies the determinant by the sign of
  29. Particular, if two nodes are joined by an edge, so are their images under the, permutation , * For relations, see relation-preserving automorphism. * In topology
  30. Of Diff (M) that preserves all the components of M, and Σ (π0M) is the, permutation ,group of the set π0M (the components of M). Moreover, the image of the map is
  31. A permutation of the rows multiplies the determinant by the sign of the, permutation , #Adding a scalar multiple of one column to another column does not change the
  32. Group of the extension. * In graph theory an automorphism of a graph is a, permutation ,of the nodes that preserves edges and non-edges. In particular, if two nodes
  33. Boxes in the next round. The alternation of substitution from the S-boxes, and, permutation , of bits from the P-box and E-expansion provides so-called" confusion and
  34. A new or emerging area of application will commonly be defined temporarily as a, permutation ,or subset of existing disciplines; there is often gray area as to when a given
  35. Arrangement in which no dots are raised. For reference purposes, a particular, permutation ,may be described by naming the positions where dots are raised, the positions
  36. Gave several important theorems in complex analysis and initiated the study of, permutation ,groups in abstract algebra. A profound mathematician, Cauchy exercised a great
  37. Skew-symmetric. That is, : x_, x_, x_ = \SGN (\sigma)x_1,x_2,x_3 for any, permutation ,σ. It follows that: x, y,x = 0 for all x and y. This is equivalent to the
  38. Its first k elements. There are many duplicate selections: any combined, permutation ,of the first k elements among each other, and of the final (n − k) elements
  39. e.g. the definitions of isomorphism, homeomorphism, diffeomorphism, permutation ,group, and projective map. A bijective function from a set to itself is also
  40. Of the cipher AES is based on a design principle known as a Substitution, permutation ,network. It is fast in both software and hardware. Unlike its predecessor, DES
  41. Prod_in A_. \ Here the sum is computed over all permutation s σ of the set A, permutation ,is a function that reorders this set of integers. The position of the element i
  42. Expansion — the 32-bit half-block is expanded to 48 bits using the expansion, permutation , denoted E in the diagram, by duplicating half of the bits. The output consists
  43. Of no numbers at all is 1. This is useful because: * There is exactly one, permutation ,of zero objects (with nothing to permute," everything" is left in place). *
  44. An in terms of a lower triangular matrix L, an upper triangular matrix U and a, permutation ,matrix P:: A = PLU. \, The determinants of L and U can be quickly calculated
  45. Have exactly the same effect, the F-test's p-values closely approximate the, permutation ,test's p-values: The approximation is particularly close when the design is
  46. Stages of processing, termed rounds. There is also an initial and final, permutation , termed IP and FP, which are inverses (IP" undoes" the action of FP, and
  47. The approximation is particularly close when the design is balanced. Such, permutation ,tests characterize tests with maximum power against all alternative hypotheses
  48. 3,2,1 results. Therefore, 3,2,1 is an odd permutation . Similarly,the, permutation ,2,3,1 is even (1,2,3 → 2,1,3 → 2,3,1,with an even number of switches
  49. Are generated depth-first, and the search space is pruned if the partial, permutation ,produces a diagonal attack. Constraint programming can also be very effective
  50. Of S and constant functions associating to each x\in S a given c\in S. Every, permutation ,of S has the codomain equal to its domain and is bijective and invertible. A

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