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Counting Necklaces

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#combinatorics #generating-functions #necklace-and-bracelets
67
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Calculate $\sum_{|S|=k}(n-|\cup S|)^m$ where $S$ is a subset of $X=\{\{a_1,a_2\},\{a_2,a_3\},\cdots,\{a_{n-1},a_n\},\{a_n,a_1\}\}$

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#combinatorics #elementary-set-theory #generating-functions #inclusion-exclusion
51
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Consider the map ψ:C[x, y]→C[t] defined by f(x, y)⇝f(t^2, t^3). Prove that its image is the set of polynomials p(t) such that dp/dt(0)=0

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#polynomials #generating-functions
171
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Relation between generating function of a sequence and reciprocal sequence

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#generating-functions #analytic-combinatorics
232
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What is the Generating Function for the sequence of reciprocal triangular numbers?

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#elementary-number-theory #generating-functions
59
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Odd derivatives of a function $f$ satisfying $f(1/z)=-f(z)$

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#combinatorics #generating-functions
154
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Finding the sum of first $N$ squares with generating functions

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#calculus #generating-functions
361
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How to compute the coefficient of a generating function?

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#combinatorics #generating-functions
306
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Generating Function For Catalan Numbers Type Sequence

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#sequences-and-series #elementary-number-theory #generating-functions #catalan-numbers #cauchy-product
431
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Does there exist a generating function for the rational numbers?

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#generating-functions #rational-numbers
175
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Are all recurrence relations solvable by generating functions? A tricky one

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#recurrence-relations #generating-functions
153
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Recurrence Relation from Generating Function: $F_{n}(x)=(\sqrt{1+x})^n$

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#recurrence-relations #generating-functions
2.4k
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How can I learn about generating functions?

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#combinatorics #generating-functions
195
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Find the coefficient of $x^{13}$ in the convolution of two generating functions

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#discrete-mathematics #generating-functions #convolution
198
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generating function for $F_{5n}/(5F_n)$

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#generating-functions #fibonacci-numbers

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