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

The word ( nk ), is the 19658 most frequently used in English word vocabulary

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  1. All natural numbers k at once by the relation: \text style (1+X)in=\sum_\bin om, nk , X^k, from which it is clear that \minor n0 \minor in 1 and \minor NK=0 for k
  2. Multiplicative) * IDK (n): the power functions, defined by IDK (n) =, nk , for any natural (or even complex) number k (completely multiplicative). As
  3. In some fixed order, which establishes a bijection from an interval of \minor, nk , integers with the set of those k-combinations. Assuming is itself ordered, for
  4. To compute individual binomial coefficients is given by the formula: \bin om, nk , \franc \franc=\prod_OK \franc, where the numerator of the first fraction is
  5. Imagine" for the 2010 Herbie Hancock album, The Imagine Project along with P!, nk , India. Are, Jeff Beck, Konono N°1,Humor Hangar and others. Personal life
  6. Two and evaluated by radix-2 Cooley–Turkey Fits, for example),via the identity, nk , = - (k-n)^2/2 + n^2/2 + k^2/2. FFT algorithms specialized for real and/or
  7. Between adjacent numbers in Pascal's triangle in all three directions:: \bin om, nk , = \bin om n \frack, \text>0,: \bin om NK = \bin om k \franc n, \text, : \bin om NK
  8. There is a sequence of circuits W1,W2,W3,..., where In is a circuit of size, nk , deciding falsifiability of all Boolean formulas whose encoding size is ≤ n. Of
  9. Constants c and k such that it can be solved in time O (logic n) using O (, nk , ) parallel processors. Stephen Cook coined the name" Nick's class" after
  10. Contain n and that do not contain n separately. It follows easily that \minor, nk ,0 when k > n, and \minor in 1 for all n, so the recursion can stop when
  11. Total number of arithmetic operations is For example, if all the values are O (, nk , ) for some k, then the time required is O (NK+2). This algorithm is easily
  12. Put m0 n0,after finitely many steps we find a NK such that NK > m0,put m1,NK, We repeat this procedure to find m2 > m1,etc. this yields an effective
  13. Binomial formula, hence its name binomial coefficient. One can define \minor, nk , for all natural numbers k at once by the relation: \text style (
  14. Numbers (taken to include 0) n and k, the binomial coefficient \minor, nk , can be defined as the coefficient of the monomial OK in the expansion of. The
  15. As a consonant. Common, if debated, assimilation includes the pronunciation of, nk , as and KZ as. Many consonant clusters can occur, up to three in
  16. Of words formed of n bits (digits 0 or 1) whose sum is k is given by \minor, nk , while the number of ways to write k=a_1+a_2+\dots+a_n where every AI is a
  17. Will be the number of such subsets. This shows in particular that \minor, nk , is a natural number for any natural numbers n and k. There are many others
  18. Axis that is different from the other two crystal axes (i.e., ni ≠ NJ =, nk , ). This unique axis is called the extraordinary axis and is also referred to as
  19. The number of k-combinations is equal to the binomial coefficient: \bin om, nk , = \franc, which can be written using factorials as \franc whenever k\LEQ n, and
  20. And denominators are cop rime and obey the recursion: Mk = OK mk−1 + mk−2:, nk , = OK nk −1 + nk −2 where m−1 n−2 1 and m−2 n−1 0 are the initial values of the
  21. Binomial coefficients have led to extending the meaning of the symbol \minor, nk , beyond the basic case where n and k are nonnegative integers with; such
  22. Recursive Formula One has a recursive formula for binomial coefficients: \bin om, nk , = \bin om + \biome \quad \born, k>0,with initial values: \bin om n0 = 1 \quad
  23. This symmetry directly, and has the merit of being easy to remember:: \bin om, nk , = \franc, where n! Denotes the factorial of n. It is obtained from the previous
  24. Sum of coefficients row The number of k-combinations for all k, \sum_\bin om, nk , = 2^n,is the sum of the nth row (counting from 0) of the binomial
  25. Called" Britney ", which was on their debut album. She is also mentioned in P!, nk , 's song" Don't Let Me Get Me ". She was cited as the inspiration of Gwyneth
  26. A most significant digit (MSD) radix sort. An LSD radix sort operates in O (, nk , ) time, where n is the number of keys, and k is the average key length. This
  27. About simultaneous congruence (see modular arithmetic). Suppose n1,n2,…, nk , are positive integers which are pairwise cop rime. Then, for any given sequence
  28. K-combinations of its elements) is given by the binomial coefficient \minor, nk , Therefore, \minor NK is often read as" n choose k ". The properties of
  29. K, \text>0,: \bin om NK = \bin om k \franc n, \text, : \bin om NK = \bin om \franc, nk , \text, k>0. Together with the basic cases \minor n0 1 \minor in, these
  30. Binomial coefficient, it is more practical to use the formula: \bin om, nk , = \franc. The numerator gives the number of k-permutations of n, i. e., of
  31. And the denominator, and canceling them out gives the relation: \bin om, nk , = \bin om n, \text0 \LE k \LE n. This expresses a symmetry that is evident from
  32. With director Penelope Spheres and starring either Zola Chanel or P!, nk , ; and an untitled film thought to be an adaptation of Laura Joplin's
  33. Of binomial coefficients Several methods exist to compute the value of \minor, nk , without actually expanding a binomial power or counting k-combinations.
  34. In all three directions:: \bin om NK = \bin om n \frack, \text>0,: \bin om, nk , = \bin om k \franc n, \text, : \bin om NK = \bin om \franc NK, \text, k>0. Together
  35. Sublist: put m0 n0,after finitely many steps we find a NK such that, nk , > m0,put m1 NK. We repeat this procedure to find m2 > m1,etc. this yields an
  36. Some algebra, that it is the largest term in the summation. But then, : \minor, nk , q^ (1-q)^ \GEQ \track since there are n+1 terms in the summation. Rearranging
  37. Coefficient also occurs (if) in the binomial formula: (x+y)in=\sum_in\bin om, nk , x^y^k (valid for any elements x, y of a commutative ring),which explains the
  38. Elements) is given by the binomial coefficient \minor NK. Therefore, \minor, nk , is often read as" n choose k ". The properties of binomial coefficients have
  39. Mk/NK is the best rational number approximation to a/b with denominator, nk , ::
  40. Is: :\franc=\franc.: This number is known as the binomial coefficient \minor, nk , because it is also the coefficient of OK in. * Factorials occur in algebra for
  41. Finally, there is a formula using factorials that is easy to remember:: \bin om, nk , = \franc \quad \box\ 0\LEQ k\LEQ n. where n! Denotes the factorial of n. This
  42. Nk = \bin om n \frack, \text>0,: \bin om NK = \bin om k \franc n, \text, : \bin om, nk , = \bin om \franc NK, \text, k>0. Together with the basic cases \minor n0 1
  43. Coefficient For integers 0 < k < n let q = n/k. Then: \track \LEQ \minor, nk , \LEQ 2^ Here is a sketch proof. Note that \minor NK QC (1-q)^ is one term of
  44. It may serve to prove a symmetry property of binomial coefficients:: :\bin om, nk , \franc \franc \franc \bin om n. Number theory Factorials have many applications in
  45. Expressions are then still called binomial coefficients. The notation \minor, nk , was introduced by Andreas von Ettingshausen in 1826,although the numbers were
  46. The binomial coefficient indexed by n and k is usually written \minor, nk , and it is the coefficient of the x k term in the polynomial expansion of the
  47. Of k-combinations for all k The number of k-combinations for all k, \sum_\bin om, nk , = 2^n,is the sum of the nth row (counting from 0) of the binomial
  48. Then: \track \LEQ \minor NK \LEQ 2^ Here is a sketch proof. Note that \minor, nk , q^ (1-q)^ is one term of the expression \sum_in \minor NI QI (1-q)^ (q + (
  49. Occurs in many other mathematical contexts, where it is denoted by \minor, nk , ; notably it occurs as coefficient in the binomial formula, hence its name
  50. Extract an increasing subsist: put m0 n0,after finitely many steps we find an, nk , such that NK > m0,put m1 NK. We repeat this procedure to find m2 > m1,etc.

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