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- 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 is6 KB (983 words) - 13:42, 8 December 2021
- * [[Generating function]]1 KB (251 words) - 15:13, 11 August 2020
- 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
- ...[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
- ==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 coe6 KB (909 words) - 15:39, 8 August 2022
- ...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
- '''Corollary 4.''' Let <math>X</math> be a generating subset of <math>G</math>. Then <math>D(G)</math> is the normal subgroup ge4 KB (688 words) - 20:11, 28 May 2008
- ...the expansion of the coefficients of the product of two polynomials (or [[generating functions]]).1 KB (190 words) - 00:57, 31 May 2016
- ...s an applied discipline, mathematicians have developed various methods for generating approximate solutions to intractable problems. The utility of such methods2 KB (322 words) - 21:03, 11 February 2009
- ...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
- ..._{n-1} + \cdots + a_kG_{n-k}</math> be a linear recurrence. Consider the [[generating function]] given by19 KB (3,412 words) - 14:57, 21 September 2022
- == 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
- 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 <ma3 KB (470 words) - 22:15, 27 August 2023
- ==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 (1,197 words) - 08:07, 15 August 2024
- ...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
- ...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+x9 KB (1,535 words) - 01:28, 16 January 2023
- Use [[generating functions]]. For each department, there is 1 way to pick 2 males, 4 ways to2 KB (328 words) - 01:26, 28 January 2023
- 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 clea949 bytes (159 words) - 03:01, 5 April 2012
- .../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 mo8 KB (1,348 words) - 09:44, 25 June 2022
- The process of choosing a block can be represented by a generating function. Each choice we make can match the 'plastic medium red circle' in3 KB (507 words) - 20:48, 6 December 2021