<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">%% if you are submitting an initial manuscript then you should have submission as an option here
%% if you are submitting a revised manuscript then you should have revision as an option here
%% otherwise options taken by the article class will be accepted
\documentclass[finalversion]{FPSAC2023}
\articlenumber{27}
%% but DO NOT pass any options (or change anything else anywhere) which alters page size / layout / font size etc

%% note that the class file already loads {amsmath, amsthm, amssymb}
\usepackage{mathtools}
\usepackage{tikz-cd}
\usepackage{tikz}
\usepackage{array}
\usetikzlibrary{decorations.markings}
\usepackage{amsfonts}
\usepackage{todonotes}
\usepackage[utf8]{inputenc}
\usepackage{ytableau}
\usepackage{subcaption}
\usepackage[export]{adjustbox}
\usepackage{mathdots}
\usepackage{comment}

\newtheorem{theorem}{Theorem}[section]
\newtheorem{prop}[theorem]{Proposition}
\newtheorem{conj}[theorem]{Conjecture}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{cor}[theorem]{Corollary}

\theoremstyle{definition}
\newtheorem{ex}[theorem]{Example}
\newtheorem{quest}[theorem]{Question}
\newtheorem{prob}[theorem]{Problem}
\newtheorem{defin}[theorem]{Definition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{claim}[theorem]{Claim}

\makeatletter
\newcommand\circled[1]{%
  \mathpalette\@circled{#1}%
}
\newcommand\@circled[2]{%
  \tikz[baseline=(math.base)] \node[draw,circle,inner sep=1pt] (math) {$\m@th#1#2$};%
}
\makeatother

\DeclareMathOperator{\Red}{Red}
\DeclareMathOperator{\Inv}{Inv}
\DeclareMathOperator{\SYT}{SYT}
\DeclareMathOperator{\SDT}{SDT}
\DeclareMathOperator{\BS}{BS}
\DeclareMathOperator{\rk}{rk}
\DeclareMathOperator{\ro}{ro}
\DeclareMathOperator{\sh}{sh}

%% define your title in the usual way
\title{Balanced Shifted Tableaux}

%% define your authors in the usual way
%% use \addressmark{1}, \addressmark{2} etc for the institutions, and use \thanks{} for contact details
\author{Jiyang Gao\thanks{\href{mailto:jgao@math.harvard.edu}{jgao@math.harvard.edu}.}\addressmark{1}, Shiliang Gao\thanks{\href{mailto:sgao23@illinois.edu}{sgao23@illinois.edu}. Shiliang Gao was partially supported by NSF Graduate Research Fellowship under grant No. DGE-1746047.}\addressmark{2}, \and Yibo Gao\thanks{\href{mailto:gaoyibo@umich.edu}{gaoyibo@umich.edu}.}\addressmark{3}}

%% then use \addressmark to match authors to institutions here
\address{\addressmark{1}Department of Mathematics, Harvard University, Cambridge, MA 02138 \\ \addressmark{2}Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 \\ \addressmark{3}Department of Mathematics, University of Michigan, Ann Arbor, MI 48104}

%% put the date of submission here
\received{\today}

%% leave this blank until submitting a revised version
%\revised{}

%% put your English abstract here, or comment this out if you don't have one yet
%% please don't use custom commands in your abstract / resume, as these will be displayed online
%% likewise for citations -- please don't use \cite, and instead write out your citation as something like (author year)
\abstract{We introduce balanced shifted tableaux, as an analogue of balanced tableaux of Edelman and Greene, from the perspective of root systems of type $B$ and $C$. We show that they are equinumerous to standard Young tableaux of the corresponding shifted shape by presenting an explicit bijection.}

%% put your French abstract here, or comment this out if you don't have one
% \resume{\lipsum[2]}

%% put your keywords here, or comment this out if you don't have them yet
\keywords{balanced tableaux, standard Young tableaux, Edelman-Greene insertion}

%% you can include your bibliography however you want, but using an external .bib file is STRONGLY RECOMMENDED and will make the editor's life much easier
%% regardless of how you do it, please use numerical citations; i.e., [xx, yy] in the text

%% this sample uses biblatex, which (among other things) takes care of URLs in a more flexible way than bibtex
%% but you can use bibtex if you want
\usepackage[backend=bibtex]{biblatex}
\addbibresource{ref.bib}
%% note the \printbibliography command at the end of the file which goes with these biblatex commands

\begin{document}

\maketitle
%% note that you DO NOT have to put your abstract here -- it is generated by \maketitle and the \abstract and \resume commands above

\input{1-Intro}
\input{2-Prelim}
\input{3-Trapezoid}
\input{4-Kraskiewicz}
\input{5-General}

% \section{A section}

% \lipsum[3]

% \begin{equation}\label{eqn:eq1}
% \int_0^\infty \exp(-x) \, \mathrm{d}x = 1.
% \end{equation}

% \begin{lem}\label{lem:lem1}
% \lipsum[11]
% \end{lem}

% \lipsum[10]

% \begin{figure}
% \centering
% \includegraphics[width=0.5\textwidth]{plot}
% \caption{A plot of a function.}
% \label{fig:plot}
% \end{figure}

% \subsection{A subsection}

% \lipsum[5]

% \begin{align*}
% 1 + 1 + 1 &amp;= 2 + 1 \\ &amp;= 3.
% \end{align*}

% \subsubsection{A subsubsection}

% \lipsum[17]

% Here is a citation~\cite{greenwade93} with URL. Here is another
% citation~\cite{MR4}, which is the earliest-numbered Math Review with a
% functioning DOI: MR0000004. Finally, a reference to
% equation~\eqref{eqn:eq1}. And a reference to Figure~\ref{fig:plot}.

\acknowledgements{We are grateful to Alex Yong, Jianping Pan and Zachary Hamaker for helpful conversation.}

%% if you use biblatex then this generates the bibliography
%% if you use some other method then remove this and do it your own way
\printbibliography



\end{document}
</pre></body></html>