\magnification \magstep1
\nopagenumbers

%%%% Corollary to the general cubic identity

$$
R_n = 0\ (n\geq2) \quad \Rightarrow \quad
\mu_1^2 \mu_n = \mu_n \sum_{i=0}^{n-1}
({\rm id}^{\otimes i} \otimes \mu_1^2 \otimes {\rm id}^{\otimes n-1-i})
$$

\bye

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%% html tag

%%%% <img src="images/assoc2.png"
%%%%      title="Corollary to the general cubic identity"
%%%%      alt="A corollary to the general cubic identity"
%%%%      width="791" height="88">

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%% png creation (normal size, transparent)

%%% pdftex assoc2.tex
%%% pdftocairo -png -singlefile -transp -r 180 assoc2.pdf tmp
%%% magick -define png:exclude-chunk=date,time tmp.png -trim +repage assoc2.png
%%% optipng assoc2.png

%%%% magick adds white (fallback) background to the transparent image
%%%% and has the convenient option -trim.

%%%% Image size is 791x88.

%% program versions

%%% This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019/Debian) (preloaded format=pdftex 2024.3.16)

%%% pdftocairo version 0.86.1
%%% ImageMagick 7.1.1-43 Q16-HDRI x86_64 22550 https://imagemagick.org
%%% OptiPNG version 0.7.7

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%%%% Created:
%%% 2025-10-27

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