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%       NOTE THAT \th HAS BEEN RENEWCOMMANDed
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\newcommand{\Ze}{\Zeta}


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\newcommand{\Ub}{\ol{U}}
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\newcommand{\yb}{\ol{y}}
\newcommand{\Yb}{\ol{Y}}
\newcommand{\zb}{\ol{z}}
\newcommand{\Zb}{\ol{Z}}
\newcommand{\pib}{\ol{\pi}}
\newcommand{\sib}{\ol{\si}}
\newcommand{\degb}{\ol{\deg}}
\newcommand{\vj}{\vec{\jmath}}
\newcommand{\vr}{\vec{r}}
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\newcommand{\vw}{\vec{w}}
\newcommand{\ttab}{\{t\}}
\newcommand{\stab}{\{s\}}


\newcommand{\Age}{\operatorname{Age}}
\newcommand{\Aut}{\operatorname{Aut}}
\newcommand{\abl}{\operatorname{al}}
\newcommand{\BC}{\operatorname{BC}}
\newcommand{\capa}{\operatorname{cap}}
\newcommand{\codim}{\operatorname{codim}}
\newcommand{\ch}{\operatorname{ch}}
%Commented out \ch for choose
\newcommand{\col}{\operatorname{col}}
\newcommand{\ctt}{\operatorname{ct}}
\newcommand{\Der}{\operatorname{Der}}
\newcommand{\des}{\operatorname{des}}
\newcommand{\Des}{\operatorname{Des}}
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\newcommand{\pfa}{\operatorname{pf}}
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\newcommand{\scz}{\scriptsize}
\newcommand{\cho}{\choose}

\newcommand{\Schu}{Sch\"utzenberger}
\newcommand{\aim}{Adv.\ in Math.\/}
\newcommand{\bams}{Bull.\ Amer.\ Math.\ Soc.\/}
\newcommand{\cjm}{Canad.\ J. Math.\/}
\newcommand{\dm}{Discrete Math.\/}
\newcommand{\dmj}{Duke Math.\ J.\/}
\newcommand{\ejc}{European J. Combin.\/}
\newcommand{\jaa}{J. Algebra\/}
\newcommand{\jac}{J. Algebraic Combin.\/}
\newcommand{\jas}{J. Algorithms\/}
\newcommand{\jams}{J. Amer.\ Math.\ Soc.\/}
\newcommand{\jct}{J. Combin.\ Theory\/}
\newcommand{\jcta}{J. Combin.\ Theory Ser. A\/}
\newcommand{\jctb}{J. Combin.\ Theory Ser. B\/}
\newcommand{\jgt}{J. Graph Theory\/}
\newcommand{\jram}{J. Reine Angew.\ Math.\/}
\newcommand{\pjm}{Pacific J. Math.\/}
\newcommand{\pams}{Proc.\ Amer.\ Math.\ Soc.\/}
\newcommand{\plms}{Proc.\ London Math.\ Soc.\/}
\newcommand{\tams}{Trans.\ Amer.\ Math.\ Soc.\/}
\newcommand{\pja}{Proc.\ Japan Acad.\ Ser.\ A  Math\/}
\newcommand{\sv}{Springer-Verlag Lecture Notes in Math.\/}
\newcommand{\crgs}{Combinatoire et Repr\'{e}sentation du 
    Groupe Sym\'{e}trique, Strasbourg 1976, D. Foata ed.}
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\newcommand{\oup}{Oxford University Press} 
\newcommand{\pr}{preprint}
\newcommand{\ip}{in preparation}
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