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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:
w:en:Creative Commons
attribution share alike
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Captions

A plot of the Eulerian numbers

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depicts

3 August 2023

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Date/TimeThumbnailDimensionsUserComment
current19:39, 3 August 2023Thumbnail for version as of 19:39, 3 August 20231,338 × 1,251 (2.85 MB)WalkingRadianceUploaded own work with UploadWizard

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