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• Generating function
  ...a [[sequence]] which is of interest. Therefore the power series (i.e. the generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdots </math> and the sequence Many generating functions can be derived using the [[Geometric sequence#Infinite|sum formul
  4 KB (659 words) - 12:54, 7 March 2022
• Generating functions
  #REDIRECT [[Generating function]]
  33 bytes (3 words) - 12:35, 6 July 2007

Page text matches

• Combinatorics
  ...s competitions and can be approached by a variety of techniques, such as [[generating functions]] or the [[Principle of Inclusion-Exclusion|principle of inclusio
  1 KB (208 words) - 02:12, 4 October 2020
• Combination
  * [[Generating function]]
  4 KB (615 words) - 11:43, 21 May 2021
• San Diego ARML
  ...k Tiefenbruck]] and is supported by the [[San Diego Math Circle]]. [[user:generating | Andy Niedermaier]] was a coach for 2007-2009, and [[user:MCrawford | Math
  2 KB (378 words) - 16:34, 5 January 2010
• Generating function
  ...a [[sequence]] which is of interest. Therefore the power series (i.e. the generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdots </math> and the sequence Many generating functions can be derived using the [[Geometric sequence#Infinite|sum formul
  4 KB (659 words) - 12:54, 7 March 2022
• Binomial Theorem
  ...function are termwise equal, the series at <math>x = a + b</math> is the [[Generating function#Convolutions|convolution]] of the series at <math>x = a</math> and
  5 KB (935 words) - 13:11, 20 February 2024
• Prime number
  The [[Sieve of Eratosthenes]] is a relatively simplistic [[algorithm]] for generating a list of the first few prime numbers. It is a method in which the multiple The Sieve of Sundaram is a relatively simplistic [[algorithm]] for generating all odd prime numbers, less than <math>2n+2</math>. It is a method by which
  6 KB (985 words) - 12:38, 25 February 2024
• 2005 USAMO Problems/Problem 4
  ..._i=C_{i-1}+4i</math>, and note that <math>C_0=1</math>. Now we can create generating functions. <math>F(x)=\sum_{i=0}^\infty C_ix^i</math>. Also, <math>G(x)=\
  7 KB (1,276 words) - 20:51, 6 January 2024
• 2006 AMC 12A Problems/Problem 24
  Alternatively, we can use a [[generating function]] to solve this problem. The goal is to find the generating function for the number of unique terms in the simplified expression (in te
  8 KB (1,332 words) - 17:37, 17 September 2023
• Combinatorics/Intermediate
  * [[Generating functions]]
  910 bytes (77 words) - 16:23, 18 May 2021
• 1985 AIME Problems/Problem 12
  == Solution 6 (Generating Functions and Roots of Unity Filter / Casework) == .../math> states, <math>n</math> steps) is <math>(x+x^2+x^3)^n</math>, so the generating function of interest for this problem is <math>(x+x^2+x^3)^7</math>. Our go
  17 KB (2,837 words) - 13:34, 4 April 2024
• 1992 AIME Problems/Problem 13
  ...th> can be equal with some value of <math>x</math>). MAA is pretty good at generating smooth combinations, so in this case, the AM-GM works; however, always try
  4 KB (703 words) - 02:40, 29 December 2023
• 1996 AIME Problems/Problem 3
  == Solution 2 (Generating Functions)==
  3 KB (515 words) - 04:29, 27 November 2023
• 1998 AIME Problems/Problem 7
  ...for each of the terms, and obtain <math>(x+x^3+x^5\cdots)^4</math> as the generating function for the sum of the <math>4</math> numbers. We seek the <math>x^{98
  5 KB (684 words) - 11:41, 13 August 2023
• 2003 AIME II Problems/Problem 13
  ===Solution 6 (generating functions)=== The generating function for this is <math>(x+x^2)</math> since an ant on any vertex of the
  15 KB (2,406 words) - 23:56, 23 November 2023
• 2006 USAMO Problems/Problem 5
  ...+1}</math>, <math>M\geq 0</math> be the length of the longest jump made in generating <math>J_{i_0,k_0}</math>. Such a jump can only be made from a number that i
  7 KB (1,280 words) - 17:23, 26 March 2016
• Vector space
  == Generating Subset == ...ubset is said to be ''minimal'' if on removing any element it ceases to be generating.
  3 KB (561 words) - 00:47, 21 March 2009
• Combinatorics/Olympiad
  * [[Generating functions]]
  705 bytes (64 words) - 16:22, 18 May 2021
• 2005 Alabama ARML TST Problems/Problem 1
  We use [[generating function]]s to represent the sum of the two dice rolls: <center><math>(x+x^
  1 KB (210 words) - 01:30, 3 January 2023
• 2007 AIME I Problems/Problem 10
  ...n if two squares in the row are shaded, then the row is represented by the generating function <math>ab+ac+ad+bc+bd+cd</math>, which we can write as <math>P(a,b,
  13 KB (2,328 words) - 00:12, 29 November 2023
• 2006 AIME II Problems/Problem 10
  We can apply the concept of generating functions here. ...function for the next 5 games is <math>(1 + x)^{5}</math>. Thus, the total generating function for number of games he wins is
  6 KB (983 words) - 13:42, 8 December 2021

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