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• Lucas' Theorem
  * [[Generating function]]
  1 KB (251 words) - 15:13, 11 August 2020
• 2005 Alabama ARML TST Problems/Problem 12
  The [[generating function]] for <math>a, b, c,</math> and <math>d</math> is <math>x+x^2+x^3+
  1 KB (172 words) - 09:56, 18 June 2008
• Partition (combinatorics)
  ...[Jacobi theta function]], in particular the [[Jacobi triple product]]. The generating function approach and the theta function approach can be used to study many == Generating Functions ==
  10 KB (1,508 words) - 14:24, 17 September 2017
• 2008 AIME I Problems/Problem 9
  ==Solution 3 (Generating Functions)== We can model this as the generating function <cmath>\left(x^3+x^4+x^6\right)^{10}</cmath> where we want the coe
  6 KB (909 words) - 15:39, 8 August 2022
• Free magma
  ...math> to <math>M(X)</math>, and let <math>(u_{i},v_i)_{i\in I}</math> be a generating set of the equivalence relation <math>R(x,y)</math> defined as <math>f(x) =
  4 KB (887 words) - 13:19, 6 July 2016
• Derived group
  '''Corollary 4.''' Let <math>X</math> be a generating subset of <math>G</math>. Then <math>D(G)</math> is the normal subgroup ge
  4 KB (688 words) - 20:11, 28 May 2008
• 2008 Mock ARML 2 Problems/Problem 8
  ...the expansion of the coefficients of the product of two polynomials (or [[generating functions]]).
  1 KB (190 words) - 00:57, 31 May 2016
• Approximation Techniques
  ...s an applied discipline, mathematicians have developed various methods for generating approximate solutions to intractable problems. The utility of such methods
  2 KB (322 words) - 21:03, 11 February 2009
• Alternating permutation
  ...tangent]] numbers. These latter names are the result of the remarkable [[generating function]] (or equivalently [[Taylor series]]) [[identity]]
  2 KB (246 words) - 12:50, 6 August 2009
• Characteristic polynomial
  ..._{n-1} + \cdots + a_kG_{n-k}</math> be a linear recurrence. Consider the [[generating function]] given by
  19 KB (3,412 words) - 14:57, 21 September 2022
• 2003 AMC 12A Problems/Problem 22
  == Solution 2 (Generating Functions) == ...r horizontally is equally likely, we can write all the possible paths as a generating function:
  2 KB (321 words) - 08:40, 30 June 2023
• 2010 AIME I Problems/Problem 4
  This can be solved quickly and easily with [[generating functions]]. The generating functions for these coins are <math>(1+x)</math>,<math>(1+x)</math>,and <ma
  3 KB (470 words) - 22:15, 27 August 2023
• 2010 AIME I Problems/Problem 10
  ==Solution 5: Generating Functions== We will represent the problem using generating functions. Consider the generating function <cmath>f(x) = (1+x^{1000}+x^{2000}+\cdots+x^{99000})(1+x^{100}+x^{
  7 KB (1,147 words) - 21:58, 23 January 2024
• 2010 AIME II Problems/Problem 11
  ...the first, second, third respective squares are <math>1</math>'s. Then the generating function representing the possible events that exclude a row of <math>1,1,1 Therefore, the generating function representing the possible grids where no row is filled with <math>
  6 KB (1,057 words) - 01:58, 8 January 2023
• 2011 AIME II Problems/Problem 6
  ...h>a,x,y,k,b.</math> Now we use generating functions to finish. We find the generating function of the whole expression is <math>(x + x^2 + \cdots)^4 \cdot (x^2+x
  9 KB (1,535 words) - 01:28, 16 January 2023
• 2012 AIME II Problems/Problem 3
  Use [[generating functions]]. For each department, there is 1 way to pick 2 males, 4 ways to
  2 KB (328 words) - 01:26, 28 January 2023
• Mock AIME II 2012 Problems/Problem 5
  Consider the generating function for a 12 sided die. When rolled n times, the generating function is <math>(x^1+x^2+\hdots+x^{12})^n</math>. This polynomial is clea
  949 bytes (159 words) - 03:01, 5 April 2012
• 1988 USAMO Problems/Problem 5
  .../math> of two elements, and on the left, we have the factorisation of this generating function that considers the breakdown of any given monic polynomial into mo
  8 KB (1,348 words) - 09:44, 25 June 2022
• 1989 AHSME Problems/Problem 22
  The process of choosing a block can be represented by a generating function. Each choice we make can match the 'plastic medium red circle' in
  3 KB (507 words) - 20:48, 6 December 2021
• 2014 AIME I Problems/Problem 11
  ==Solution 5 (Generating Functions)==
  11 KB (1,677 words) - 23:54, 4 February 2022

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