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I am writing a paper with a coauthor who is at the same institution. What is the standard way to add affiliation (which is the same for both) and email addresses for the document in the article class format?

Thanks!

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The article class has no particular provisions for multiple authors, affiliations etc. How this information is arranged, is usually defined by the publisher or editor, who in most cases also provides a class file that takes care of typesetting the header. Otherwise it is you, the author, who decides how this information should be arranged. Just look around at different publications, choose a design that you like, and then try to imitate it (or ask how to do it).

E.g., with the article class you could do it like that (I have cut down the image a bit, so the length of the page does not correspond to the code):

\documentclass{article}
\begin{document}
\title{The Title of the Paper}
\author{X. First\thanks{Email: [email protected]}~ 
   and Y. Second\thanks{Email: [email protected]}\\
   The Common Affiliation}
\date{September 2016}
\maketitle
\end{document}

enter image description here

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