%%%%%%%%%%%% PACKAGES %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\usepackage{upref}
\usepackage{float}
\usepackage{url}
\usepackage{enumerate}
\usepackage{array}
\usepackage{tikz}
\usetikzlibrary{positioning, shapes.geometric}
\usepackage{xcolor}

\definecolor{lgreen} {RGB}{180,210,100}
\definecolor{dblue}  {RGB}{20,66,129}
\definecolor{ddblue} {RGB}{11,36,69}
\definecolor{lred}   {RGB}{220,0,0}
\definecolor{nred}   {RGB}{224,0,0}
\definecolor{norange}{RGB}{230,120,20}
\definecolor{nyellow}{RGB}{255,221,0}
\definecolor{ngreen} {RGB}{98,158,31}
\definecolor{dgreen} {RGB}{78,138,21}
\definecolor{nblue}  {RGB}{28,130,185}
\definecolor{jblue}  {RGB}{20,50,100}

%%%%%%%%%%%% THEOREMS AND RELATED STRUCTURES %%%%%%%%%%%%%%%%%%
\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem*{theorem*}{Theorem}
\newtheorem*{main}{Main theorem}
\newtheorem{problem}[theorem]{Problem}

\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{example}[theorem]{Example}
\newtheorem{convention}[theorem]{Convention}
\newtheorem{question}[theorem]{Question}
\newtheorem{remark}[theorem]{Remark}

%%%%%%%%%%%% COMMANDS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand*\conv{\ensuremath{\text{\normalfont{conv}}}}
\renewcommand*\O{\mathcal{O}}
\newcommand*\concat{\cdot}
\newcommand*\nconcat{\odot}

\def\reals{{\mathbb R}}
\def\rationals{{\mathbb Q}}
\def\naturals{{\mathbb Z}_{>0}}
\def\complex{{\mathbb C}\/}
\def\integers{{\mathbb Z}}

\newcommand{\1}{\mathbf{1}}
\newcommand{\id}{\mathrm{id}} % identity map
\newcommand{\spF}{\mathrm{F}} % general set species
\newcommand{\spOP}{\mathrm{OP}} % set species of orbit polytopes
\newcommand{\OPbar}{\overline{\mathrm{OP}}} % set species of orbit polytopes up to normal equivalence
\newcommand{\vF}{\mathbf{F}} % general vector species
\newcommand{\vOP}{\mathbf{OP}} % vector species of orbit polytopes
\newcommand{\Comp}{\mathrm{Comp}} % set species of compositions
\newcommand{\Comphat}{\mathrm{\widehat{Comp}}} % set species of compositions with more than one part
\newcommand{\OP}{\overline{\mathbf{OP}}} % Vector species of orbit polytopes up to normal equivalence

\newcommand{\rH}{\mathrm{H}} % general Hopf monoid in set species
\newcommand{\vH}{\mathbf{H}} % general Hopf monoid in vector species
\newcommand{\rGP}{\mathrm{GP}} % Hopf monoid of gps in set species
\newcommand{\Hcomp}{\mathit{Comp}} % Hopf algebra of compositions

\endinput