% Packages
\usepackage{enumerate}            % more powerful enumerate environments
\usepackage{microtype}            % nicer text spacing
\usepackage{mathtools}            % \coloneqq, etc.
\usepackage{thmtools}             % interface to amsthm
%\usepackage{hyperref}             % url's
\usepackage[enableskew]{youngtab} % \young
%\usepackage{cleveref}             % \Cref

% Math operators
\DeclareMathOperator{\Ch}{ch}
\DeclareMathOperator{\comaj}{comaj}
\DeclareMathOperator{\cont}{cont}
\DeclareMathOperator{\des}{des}
\DeclareMathOperator{\Des}{Des}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\F}{F}
\DeclareMathOperator{\flex}{flex}
\DeclareMathOperator{\freq}{freq}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\KW}{KW}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\lex}{lex}
\DeclareMathOperator{\bfmaj}{\mathbf{maj}}
\DeclareMathOperator{\maj}{maj}
\DeclareMathOperator{\mash}{mash}
\DeclareMathOperator{\M}{M}
\DeclareMathOperator{\N}{N}
\DeclareMathOperator{\NF}{NF}
\DeclareMathOperator{\NFD}{NFD}
\DeclareMathOperator{\OFD}{OFD}
\DeclareMathOperator{\ot}{\otimes}
\DeclareMathOperator{\Par}{Par}
\DeclareMathOperator{\period}{period}
\DeclareMathOperator{\PP}{P}
\DeclareMathOperator{\rad}{rad}
\DeclareMathOperator{\RSK}{RSK}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sh}{sh}
\DeclareMathOperator{\Span}{Span}

\DeclareMathOperator{\Stab}{Stab}
\DeclareMathOperator{\SSYT}{SSYT}
\DeclareMathOperator{\stat}{stat}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\SYT}{SYT}
\DeclareMathOperator{\W}{W}
\DeclareMathOperator{\wgt}{wt}
\DeclareMathOperator{\x}{\times}

% Convenient shortcuts
\newcommand{\bC}{\mathbb{C}}
\newcommand{\bQ}{\mathbb{Q}}
\newcommand{\bZ}{\mathbb{Z}}
\newcommand{\cO}{\mathcal{O}}
\newcommand{\cL}{\mathcal{L}}
\newcommand{\fU}{\mathfrak{U}}

\newcommand{\ind}{\mathord{\uparrow}}
\newcommand{\f}{\frac}
\newcommand{\lm}{\lambda}
\newcommand{\lam}{\lambda}
\newcommand{\pa}[1]{{\left( {#1}\right)}}
\newcommand{\sub}{\subset}
\newcommand{\al}{\alpha}
\newcommand{\8}{\infty}
\newcommand{\es}{\emptyset}
\newcommand{\D}{\Delta}
\newcommand{\de}{\delta}
\newcommand{\be}{\beta}
\newcommand{\w}{\omega}
\newcommand{\s}{\sigma}
\newcommand{\si}{\sigma}
\newcommand{\sube}{\subseteq}
\newcommand{\g}{\gamma}
\newcommand{\ep}{\epsilon}
\newcommand{\dd}{\cdot}
\newcommand{\tx}{\text}
\newcommand{\ti}{\tilde}
\newcommand{\sm}{\setminus}
\newcommand{\lp}{\left(}
\newcommand{\rp}{\right)}
\newcommand{\lb}{\{\!\!\{}
\newcommand{\rb}{\}\!\!\}}
\newcommand{\la}{\langle}
\newcommand{\ra}{\rangle}
\newcommand{\ch}{\binom}
\newcommand{\imp}{\implies}
\newcommand{\va}{\varphi}
\newcommand{\vn}{\varnothing}
\newcommand{\un}{\underline}
\newcommand{\ul}{\underline{\lam}}
\newcommand{\udot}{\dot{\,}}
\newcommand{\bfx}{\mathbf{x}}

% Convenient general macros

\newcommand{\too}[1]{\stackrel{#1}{\to}}
\newcommand{\mch}[2]{%
  \left.\mathchoice%
    {\left(\kern-0.48em\ch{#1}{#2}\kern-0.48em\right)}
    {\big(\kern-0.30em\ch{\smash{#1}}{\smash{#2}}\kern-0.30em\big)}
    {\left(\kern-0.30em\ch{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
    {\left(\kern-0.30em\ch{\smash{#1}}{\smash{#2}}\kern-0.30em\right)}
  \right.
}

\theoremstyle{plain}
\newtheorem{Theorem}{Theorem}[section]
\newtheorem*{Theorem*}{Theorem}
\newtheorem{Lemma}[Theorem]{Lemma}
\newtheorem{Proposition}[Theorem]{Proposition}
\newtheorem{Corollary}[Theorem]{Corollary}
\newtheorem{Problem}[Theorem]{Problem}

\theoremstyle{definition}
\newtheorem{Notation}[Theorem]{Notation}
\declaretheorem[style=definition,sibling=Theorem]{Definition}
\newtheorem{Example}[Theorem]{Example}
\newtheorem{Remark}[Theorem]{Remark}