Tag: Combinatorics

• add

  maths/combinatorics/arithmetic

  Performs the addition of two long positive integers in the given base.

• Ascending_Subsequence

  maths/combinatorics/permutations

  Finds the longest ascending subsequence of a permutation.

• ASM_Number

  maths/combinatorics/sequences

  Returns the number of alternating sign matrices of the given order.

• ASM_Triangle_Row

  maths/combinatorics/sequences

  Returns a row of the alternating sign matrix triangle.

• bell_numbers_list

  maths/combinatorics/sequences

  Returns the Bell numbers of order 0 to n.

• Binomial_Coefficient

  maths/combinatorics/arithmetic

  Returns the binomial coefficient using the factorial function.

• binomial_coefficient_gamma

  maths/combinatorics/arithmetic

  Computes the binomial coefficient with the given arguments.

• Breaks

  maths/combinatorics/permutations

  Counts the number of breaks in a permutation.

• Catalan_Numbers_List

  maths/combinatorics/sequences

  Computes the Catalan numbers, of order 0 to n.

• Catalan_Triangle_Row

  maths/combinatorics/sequences

  Computes the row of the given order in Catalan's triangle.

• Check

  maths/combinatorics/permutations

  Checks whether an array represents a permutation.

• Cube_Root

  maths/combinatorics/arithmetic

  Returns the cube root of the argument, which may be negative.

• Cycles

  maths/combinatorics/permutations

  Counts the number of cycles in a permutation.

• Derangements_List

  maths/combinatorics/sequences

  Returns the number of derangements of 0 through \e n objects.

• Derangements_Number

  maths/combinatorics/sequences

  Calculates the number of derangements of \e n objects.

• Derangement_Check

  maths/combinatorics/permutations

  Verifies if a given permutation is a derangement.

• Euler_Triangle_Row

  maths/combinatorics/sequences

  Computes the row of order \e n in the Euler triangle.

• Expx2

  maths/combinatorics/arithmetic

  Computes the exponential of a squared argument.

• Exp_Sub1

  maths/combinatorics/arithmetic

  Exponentiates a number and subtracts 1.

• Factorial

  maths/combinatorics/arithmetic

  Calculates the factorial of an integer number.

• falling_factorial

  maths/combinatorics/arithmetic

  Calculates the falling factorial with arguments \e x and \e n.

• fixed_permutation

  maths/combinatorics/sequences

  Calculates the number of permutations of \e n objects with \e m fixed.

• gcd

  maths/combinatorics/arithmetic

  Compute the greatest common divisor of two values. <span align="right" style="background-color:99FF99"><strong>Excel: GCD</strong></span>

• inverse

  maths/combinatorics/permutations

  Calculates the inverse of the given permutation.

• Inverse_Large

  maths/combinatorics/permutations

  Calculates the inverse of the given permutation.

• Inversion_Sequence

  maths/combinatorics/permutations

  Computes the inversion sequence of a permutation.

• Involution_Numbers_List

  maths/combinatorics/sequences

  Calculates the numbers of involutions of 0 through \e n objects.

• karatsuba

  maths/combinatorics/arithmetic

  Main Karatsuba recursive algorithm

• Ln_Add1

  maths/combinatorics/arithmetic

  Evaluates the natural logarithm of a number + 1.

• log_binomial

  maths/combinatorics/arithmetic

  Calculates the logarithm of the binomial coefficient with given arguments.