File:EulerianNumberPlot.svg
Original file (SVG file, nominally 1,338 × 1,251 pixels, file size: 2.85 MB)
Captions
Captions
Summary
[edit]
| 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
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- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- 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.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:39, 3 August 2023 | | 1,338 × 1,251 (2.85 MB) | WalkingRadiance (talk | contribs) | Uploaded own work with UploadWizard |
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