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Number of partitions in decreasing order

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#combinatorics #number-theory #analytic-combinatorics
203
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Prove that the no. of selections of n things from two sets of n identical things and n other distinct things is (n+2)×2^(n-1)

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#combinatorics #combinations #combinatorial-proofs #analytic-combinatorics
246
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Integer solutions to $a_1+a_2+a_3+\cdots a_n = N$, where $l_i \leq a_i \leq r_i$ for each $i=1,2,\ldots,n$

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#combinatorics #algebra-precalculus #combinatorial-number-theory #analytic-combinatorics
100
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Number of groups of order n as a series coefficient

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#sequences-and-series #finite-groups #generating-functions #groups-enumeration #analytic-combinatorics
29
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The counting GF of admissible combinatorial classes are analytic at $0$

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#reference-request #generating-functions #analytic-combinatorics
91
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Derive the number of all labelled, balanced, 2-regular bipartite graphs

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#combinatorics #graph-theory #generating-functions #bipartite-graphs #analytic-combinatorics
94
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Doubts in the construction $\text{Cyc}(\mathcal{Z})$ from symbolic method Flajolet

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#combinatorics #generating-functions #analytic-combinatorics #combinatorial-species
75
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Why should $\mathcal{A}$ not have elements of size $0$ to form $\text{Seq}(\mathcal{A})$?

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#combinatorics #generating-functions #analytic-combinatorics
41
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How to use the Singular Inversion Theorem?

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#combinatorics #complex-analysis #singularity #analytic-combinatorics
58
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How to apply the Transfer Theorem on $\frac{z}{1-z-z^2}$ and $\frac{1+z-\sqrt{z^2-6z+1}}{4}$?

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#combinatorics #generating-functions #analytic-combinatorics
67
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Why is $\frac{1}{g(z)} \sim \frac{1}{z - z_0} \cdot \frac{1}{g'(z_0)}$ for $z_0$ a pole?

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#combinatorics #complex-analysis #analytic-combinatorics
69
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Show that $e^{z+z^3/3}$ is Hayman admissable

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#combinatorics #analytic-combinatorics
53
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How to use the implicit function scheme on $T(z) = 1 + zT(z)^2$?

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#combinatorics #generating-functions #analytic-combinatorics
87
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Derive asymptotics for $[z^n] e^{z+z^3/3}$ using saddle point approximation

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#combinatorics #analytic-combinatorics
111
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Combinatorics: How to apply the implicit function scheme?

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#combinatorics #analytic-combinatorics

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