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Probability generating function.

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#generating-functions #moment-generating-functions #eulerian-numbers
65
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Find probability: $P(X_2(t)=0|X_0(t)>0)$ where $X_i(t)$ model the population count at time $t$.

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#probability #integration #probability-theory #generating-functions
246
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Find the number of integer solutions of $x_1 + x_2 + x_3 = 16$, with $x_i \geq 0$, $x_1$ odd, $x_2$ even, $x_3$ prime.

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#combinatorics #discrete-mathematics #combinations #generating-functions
1.2k
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Find the sum of the coefficients of $x^{20}$ and $x^{21}$ in the power series expansion of $\frac 1{(1-x^3)^4}$.

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#power-series #binomial-coefficients #generating-functions
312
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Generating function of algebraic equations modulo prime powers

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#number-theory #algebraic-geometry #generating-functions #quadratic-forms
88
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When traversing a graph, what is the pmf of the degree of the next node?

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#probability-theory #graph-theory #generating-functions
212
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Remebering bell numbers

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#elementary-number-theory #generating-functions #bell-numbers
37
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Discrete math - coefficients

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#discrete-mathematics #generating-functions
310
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Extraction of coefficients of a two-variable generating function

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#binomial-coefficients #generating-functions
812
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Proving the generating functions version of Newton's identities

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#abstract-algebra #polynomials #generating-functions #symmetric-polynomials #symmetric-functions
100
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Recursive sequence with n terms

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#sequences-and-series #recurrence-relations #generating-functions #recursive-algorithms
110
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Is this mathematically valid?

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#generating-functions
324
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Prove the identity between formal power series in t

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#abstract-algebra #power-series #exponential-function #generating-functions #symmetric-polynomials
106
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Power series of a generating function

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#probability #power-series #generating-functions
107
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A limit resulting in the exponential generating function for labeled forests

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#combinatorics #generating-functions #formal-power-series

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