File:EulerianNumberPlot.svg
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Summary
| Description |
English: I created this in Mathematica. Export[File[
FileNameJoin[{$HomeDirectory, "Pictures", "EulerianNumberPlot"}]],
ComplexPlot3D[EulerianNumber[z, 5], {z, -2 - 2 I, 2 + 2 I},
PlotLegends -> Automatic, ImageSize -> Full], "SVG"]. The function EulerianNumber has the definition.
EulerianNumber//ClearAll SetAttributes[EulerianNumber,{Listable,NumericFunction}] EulerianNumber::usage="EulerianNumber[n, k] gives the number of permutations of the numbers 1 to n in which exactly k elements are greater than the previous element (permutations with k \"ascents\")"; (*This definition is based on the ResourceFunction EulerianNumber from https://resources.wolframcloud.com/FunctionRepository/resources/EulerianNumber/?i=EulerianNumber&searchapi=https%3A%2F%2Fresources.wolframcloud.com%2FFunctionRepository%2Fsearch*) EulerianNumber[n_,k_]:=Module[{x},SeriesCoefficient[(1-x)^(n+1) PolyLog[-n,x],{x,0,k}]] |
| Date | |
| Source | Own work |
| Author | WalkingRadiance |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:39, 3 August 2023 | | 1,338 × 1,251 (2.85 MB) | WalkingRadiance | Uploaded own work with UploadWizard |
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