\newcommand{\ben}{\begin{enumerate}}
\newcommand{\een}{\end{enumerate}}
\newcommand{\ble}{\begin{lem}}
\newcommand{\ele}{\end{lem}}
\newcommand{\bth}{\begin{thm}}
\renewcommand{\eth}{\end{thm}}
\newcommand{\bpr}{\begin{prop}}
\newcommand{\epr}{\end{prop}}
\newcommand{\bco}{\begin{cor}}
\newcommand{\eco}{\end{cor}}
\newcommand{\bcon}{\begin{conj}}
\newcommand{\econ}{\end{conj}}
\newcommand{\bde}{\begin{defn}}
\newcommand{\ede}{\end{defn}}
\newcommand{\bex}{\begin{exa}}
\newcommand{\eex}{\end{exa}}
\newcommand{\barr}{\begin{array}}
\newcommand{\earr}{\end{array}}
\newcommand{\btab}{\begin{tabular}}
\newcommand{\etab}{\end{tabular}}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newcommand{\bea}{\begin{eqnarray*}}
\newcommand{\eea}{\end{eqnarray*}}
\newcommand{\bal}{\begin{align*}}
\newcommand{\bce}{\begin{center}}
\newcommand{\ece}{\end{center}}
\newcommand{\bpi}{\begin{picture}}
\newcommand{\epi}{\end{picture}}
\newcommand{\bpp}{\begin{picture}}
\newcommand{\epp}{\end{picture}}
\newcommand{\bfi}{\begin{figure} \begin{center}}
\newcommand{\efi}{\end{center} \end{figure}}
\newcommand{\bprf}{\begin{proof}}
\newcommand{\eprf}{\end{proof}\medskip}
\newcommand{\capt}{\caption}
\newcommand{\bsl}{\begin{slide}{}}
\newcommand{\esl}{\end{slide}}
\newcommand{\bfr}{\begin{frame}}
\newcommand{\efr}{\end{frame}}

\newcommand{\fti}[1]{\frametitle{#1}}

\newcommand{\pscb}[1]{\pscirclebox{#1}}

%\newcommand{\ch}{\choose}
\newcommand{\bib}{thebibliography}
\newcommand{\comp}{\models}
\newcommand{\pf}{{\bf Proof.\hspace{5pt}}}
%\newcommand{\prf}{{\bf Proof\hspace{7pt}}}
%\newcommand{\qed}{\rule{1ex}{1ex}}
\newcommand{\hqed}{\hfill \qed}
\newcommand{\hqedm}{\hfill \qed \medskip}
\newcommand{\Qed}{\rule{1ex}{1ex} \medskip}
\newcommand{\qqed}{\qquad\rule{1ex}{1ex}}
\newcommand{\Qqed}{\qquad\rule{1ex}{1ex}\medskip}
\newcommand{\eqed}[1]{$\textcolor{white}{\qed}\hfill{\dil#1}\hfill\qed$}
\newcommand{\eqqed}[1]{$\rule{1ex}{0ex}\hfill{\dil#1}\hfill\qed$}
\newcommand{\mc}[3]{\multicolumn{#1}{#2}{#3}}
\newcommand{\Mc}[1]{\multicolumn{#1}{c}{}}
%\newcommand{\mc}[2]{\multicolumn{#1}{#2}}
\newcommand{\ul}{\underline}
\newcommand{\ol}{\overline}
\newcommand{\hor}{\mbox{--}}
\newcommand{\hs}[1]{\hspace{#1}}
\newcommand{\hso}[1]{\hspace{-1pt}}
\newcommand{\vs}[1]{\vspace{#1}}
\newcommand{\qmq}[1]{\quad\mbox{#1}\quad}
\newcommand{\ssk}{\smallskip}
\newcommand{\msk}{\mediumskip}
\newcommand{\bsk}{\bigskip}
\newcommand{\rp}[2]{\rule{#1pt}{#2pt}}
\newcommand{\str}[1]{\rule{#1pt}{0pt}}
%\newcommand{\st}[1]{\rule{#1}{0pt}}
\newcommand{\mbl}[1]{\makebox(0,0)[l]{#1}}
\newcommand{\mbr}[1]{\makebox(0,0)[r]{#1}}
\newcommand{\mbt}[1]{\makebox(0,0)[t]{#1}}
\newcommand{\mbb}[1]{\makebox(0,0)[b]{#1}}
\newcommand{\mbc}[1]{\makebox(0,0){#1}}
\newcommand\mar[1]{\marginpar{\raggedleft#1}}
\newcommand{\pmo}[2]{\put(#1){\makebox(0,0){#2}}}
%\newcommand{\new}[1]{\ensuremath{\blacktriangleright}#1\ensuremath{\blacktriangleleft}}
\newcommand{\emp}{\emptyset}
\newcommand{\indu}{\uparrow}
\newcommand{\rest}{\downarrow}
\newcommand{\sm}{\hspace{-2pt}\setminus\hspace{-2pt}}
\newcommand{\sbs}{\subset}
\newcommand{\sbe}{\subseteq}
\newcommand{\sps}{\supset}
\newcommand{\spe}{\supseteq}
\newcommand{\setm}{\setminus}
\newcommand{\asy}{\thicksim}
\newcommand{\dle}{<\hspace{-6pt}\cdot}
\newcommand{\dge}{\cdot\hspace{-6pt}>}
\newcommand{\lec}{\lessdot}
\newcommand{\grc}{\gtrdot}
\newcommand{\iso}{\cong}
%\newcommand{\con}{\equiv}
\newcommand{\Cong}{\equiv}
\newcommand{\conm}[1]{\stackrel{#1}{\equiv}}

\newcommand{\widevec}{\overrightarrow}
%makes a wide arrow over stuff if have \overrightarrow{stuff} 
\newcommand{\alh}{\hat{\al}}
\newcommand{\Ch}{\hat{C}}
\newcommand{\eh}{\hat{e}}
\newcommand{\Gh}{\hat{G}}
\newcommand{\ih}{\hat{\imath}}
\newcommand{\jh}{\hat{\jmath}}
\newcommand{\gh}{\hat{g}}
\newcommand{\mh}{\hat{0}}
\newcommand{\Mh}{\hat{1}}
\newcommand{\Dh}{\hat{D}}
\newcommand{\lah}{\hat{\la}}
\newcommand{\zh}{\hat{0}}
\newcommand{\oh}{\hat{1}}
\newcommand{\Ph}{\hat{P}}
\newcommand{\ph}{\hat{p}}
\newcommand{\Pih}{\hat{\Pi}}
\newcommand{\bbPh}{\hat{\bbP}}
\newcommand{\Qh}{\hat{Q}}
\newcommand{\Sh}{\hat{S}}
\newcommand{\lh}{\hat{l}}
\newcommand{\xh}{\hat{x}}
\newcommand{\Yh}{\hat{Y}}
\newcommand{\ptn}{\vdash}
\newcommand{\cpn}{\models}
\newcommand{\lt}{\lhd}
\newcommand{\gt}{\rhd}
\newcommand{\lte}{\unlhd}
\newcommand{\gte}{\unrhd}
\newcommand{\jn}{\vee}
\newcommand{\Jn}{\bigvee}
\newcommand{\mt}{\wedge}
\newcommand{\Mt}{\bigwedge}
\newcommand{\bdy}{\partial}
\newcommand{\sd}{\bigtriangleup}
\newcommand{\case}[4]{\left\{\barr{ll}#1&\mbox{#2}\\#3&\mbox{#4}\earr\right.}
\newcommand{\fl}[1]{\lfloor #1 \rfloor}
\newcommand{\ce}[1]{\lceil #1 \rceil}
\newcommand{\flf}[2]{\left\lfloor\frac{#1}{#2}\right\rfloor}
\newcommand{\cef}[2]{\left\lceil\frac{#1}{#2}\right\rceil}
\newcommand{\gau}[2]{\left[ \barr{c} #1 \\ #2 \earr \right]}
\newcommand{\gauss}[2]{\genfrac{[}{]}{0pt}{}{#1}{#2}} 
\newcommand{\setc}[2]{\{left{#1}\ :\ #2\}}
\newcommand{\setl}[2]{\{left{#1}\ |\ #2\}}
\newcommand{\qst}{$q$-Stirling numbers}
\newcommand{\qbi}{$q$-binomial coefficients}
\newcommand{\del}{\nabla}
\newcommand{\pde}[2]{\frac{\partial#1}{\partial#2}}
\newcommand{\spd}[2]{\frac{\partial^2\hspace{-2pt}#1}{\partial#2^2}}
\newcommand{\ode}[2]{\ds\frac{d#1}{d#2}}
\def\<{\langle}
\def\>{\rangle}
\newcommand{\fall}[2]{\langle{#1}\rangle_{#2}}
\newcommand{\nor}[1]{\parallel{#1}\parallel}
\newcommand{\ipr}[2]{\langle{#1},{#2}\rangle}
\newcommand{\spn}[1]{\langle{#1}\rangle}
%\newcommand{\lb}{\left\{}
%\newcommand{\rb}{\right\}}
\newcommand{\ree}[1]{(\ref{#1})}
\newcommand{\rpl}{$\longleftarrow$}

\newcommand{\ra}{\rightarrow}
\newcommand{\Ra}{\Rightarrow}
\newcommand{\lta}{\leftarrow}
\newcommand{\rla}{\leftrightarrow}
\newcommand{\lra}{\longrightarrow}
\newcommand{\lla}{\longleftarrow}
\newcommand{\Lra}{\Longrightarrow}
\newcommand{\llra}{\longleftrightarrow}
\newcommand{\Llra}{\Longleftrightarrow}
\newcommand{\ve}[1]{\stackrel{\ra}{#1}}


\newcommand{\al}{\alpha}
\newcommand{\be}{\beta}
\newcommand{\ga}{\gamma}
\newcommand{\de}{\delta}
\newcommand{\ep}{\epsilon}
\newcommand{\vep}{\varepsilon}
\newcommand{\io}{\iota}
\newcommand{\ka}{\kappa}
\newcommand{\la}{\lambda}
\newcommand{\mut}{\tilde{\mu}}
\newcommand{\om}{\omega}
\newcommand{\Phit}{\tilde{\Phi}}
\newcommand{\Psit}{\tilde{\Psi}}
\newcommand{\rhot}{\tilde{\rho}}
\newcommand{\si}{\sigma}
\renewcommand{\th}{\theta}
%       NOTE THAT \th HAS BEEN RENEWCOMMANDed
\newcommand{\ze}{\zeta}
\newcommand{\Al}{\Alpha}
\newcommand{\Ga}{\Gamma}
\newcommand{\De}{\Delta}
\newcommand{\Ep}{\epsilon}
\newcommand{\La}{\Lambda}
\newcommand{\Om}{\Omega}
\newcommand{\Si}{\Sigma}
\newcommand{\Th}{\Theta}
\newcommand{\Ze}{\Zeta}


\newcommand{\0}{{\bf 0}}
\newcommand{\1}{{\bf 1}}
\newcommand{\2}{{\bf 2}}
\newcommand{\3}{{\bf 3}}
\newcommand{\4}{{\bf 4}}
\newcommand{\5}{{\bf 5}}
\newcommand{\6}{{\bf 6}}
\newcommand{\7}{{\bf 7}}
\newcommand{\8}{{\bf 8}}
\newcommand{\9}{{\bf 9}}
\newcommand{\ba}{{\bf a}}
\newcommand{\bb}{{\bf b}}
\newcommand{\bc}{{\bf c}}
\newcommand{\bd}{{\bf d}}
\newcommand{\bfe}{{\bf e}}
\newcommand{\bff}{{\bf f}}
\newcommand{\bg}{{\bf g}}
\newcommand{\bh}{{\bf h}}
\newcommand{\bi}{{\bf i}}
\newcommand{\bj}{{\bf j}}
\newcommand{\bk}{{\bf k}}
\newcommand{\bl}{{\bf l}}
\newcommand{\bm}{{\bf m}}
\newcommand{\bn}{{\bf n}}
\newcommand{\bp}{{\bf p}}
\newcommand{\bq}{{\bf q}}
\newcommand{\br}{{\bf r}}
\newcommand{\bs}{{\bf s}}
\newcommand{\bt}{{\bf t}}
\newcommand{\bu}{{\bf u}}
\newcommand{\bv}{{\bf v}}
\newcommand{\bw}{{\bf w}}
\newcommand{\bx}{{\bf x}}
\newcommand{\by}{{\bf y}}
\newcommand{\bz}{{\bf z}}
\newcommand{\bA}{{\bf A}}
\newcommand{\bB}{{\bf B}}
\newcommand{\bC}{{\bf C}}
\newcommand{\bE}{{\bf E}}
\newcommand{\bF}{{\bf F}}
\newcommand{\bG}{{\bf G}}
\newcommand{\bH}{{\bf H}}
\newcommand{\bN}{{\bf N}}
\newcommand{\bP}{{\bf P}}
\newcommand{\bQ}{{\bf Q}}
\newcommand{\bR}{{\bf R}}
\newcommand{\bS}{{\bf S}}
\newcommand{\bT}{{\bf T}}
\newcommand{\bV}{{\bf V}}
\newcommand{\bX}{{\bf X}}
\newcommand{\bXh}{\hat{{\bf X}}}
\newcommand{\bZ}{{\bf Z}}
\newcommand{\bep}{{\bf \ep}}
\newcommand{\bcdot}{{\bf \cdot}}
\newcommand{\bmpl}{
\hspace{2pt}
\begin{pspicture}(.3,.3)
\psline[linewidth=1.5pt,arrows=cc-cc](.15,0)(.15,.3)
\psline[linewidth=1.5pt,arrows=cc-cc](0,.15)(.3,.15)
\end{pspicture}
\hspace{2pt}
}
\newcommand{\bmmi}{
\hspace{2pt}
\begin{pspicture}(.3,.3)
\psline[linewidth=1.5pt,arrows=cc-cc](0,.15)(.3,.15)
\end{pspicture}
\hspace{2pt}
}
\newcommand{\bma}{\mbox{\boldmath $a$}}
\newcommand{\bmb}{\mbox{\boldmath $b$}}
\newcommand{\bmk}{\mbox{\boldmath $k$}}
\newcommand{\bml}{\mbox{\boldmath $l$}}
\newcommand{\bmn}{\mbox{\boldmath $n$}}
\newcommand{\bbC}{{\mathbb C}}
\newcommand{\bbF}{{\mathbb F}}
\newcommand{\bbM}{{\mathbb M}}
\newcommand{\bbN}{{\mathbb N}}
\newcommand{\bbP}{{\mathbb P}}
\newcommand{\bbQ}{{\mathbb Q}}
\newcommand{\bbR}{{\mathbb R}}
\newcommand{\bbS}{{\mathbb S}}
\newcommand{\bbZ}{{\mathbb Z}}
\newcommand{\cA}{{\cal A}}
\newcommand{\cAB}{{\cal AB}}
\newcommand{\cAD}{{\cal AD}}
\newcommand{\cB}{{\cal B}}
\newcommand{\cBC}{{\cal BC}}
\newcommand{\cC}{{\cal C}}
\newcommand{\cD}{{\cal D}}
\newcommand{\cDB}{{\cal DB}}
\newcommand{\cE}{{\cal E}}
\newcommand{\cF}{{\cal F}}
\newcommand{\cG}{{\cal G}}
\newcommand{\cH}{{\cal H}}
\newcommand{\cI}{{\cal I}}
\newcommand{\cIF}{{\cal IF}}
\newcommand{\cJ}{{\cal J}}
\newcommand{\cK}{{\cal K}}
\newcommand{\cL}{{\cal L}}
\newcommand{\cm}{{\cal m}}
\newcommand{\cM}{{\cal M}}
\newcommand{\cN}{{\cal N}}
\newcommand{\cNBC}{{\cal NBC}}
\newcommand{\cO}{{\cal O}}
\newcommand{\cP}{{\cal P}}
\newcommand{\cPD}{{\cal PD}}
\newcommand{\cR}{{\cal R}}
\newcommand{\cRF}{{\cal RF}}
\newcommand{\cS}{{\cal S}}
\newcommand{\cT}{{\cal T}}
\newcommand{\cTb}{\ol{\cal T}}
\newcommand{\cV}{{\cal V}}
\newcommand{\cW}{{\cal W}}
\newcommand{\cX}{{\cal X}}
\newcommand{\cY}{{\cal Y}}
\newcommand{\cZ}{{\cal Z}}

\newcommand{\df}{\dot{f}}
\newcommand{\dF}{\dot{F}}
\newcommand{\fg}{{\mathfrak g}}
\newcommand{\fG}{{\mathfrak G}}
\newcommand{\fgt}{\tilde{\mathfrak g}}
\newcommand{\fgl}{{\mathfrak gl}}
\newcommand{\fL}{{\mathfrak L}}
\newcommand{\fS}{{\mathfrak S}}
\newcommand{\fsl}{{\mathfrak sl}}
\newcommand{\at}{\tilde{a}}
\newcommand{\ct}{\tilde{c}}
\newcommand{\dt}{\tilde{d}}
\newcommand{\pt}{\tilde{p}}
\newcommand{\Bt}{\tilde{B}}
\newcommand{\Gt}{\tilde{G}}
\newcommand{\Ht}{\tilde{H}}
\newcommand{\Kt}{\tilde{K}}
\newcommand{\Nt}{\tilde{N}}
\newcommand{\St}{\tilde{S}}
\newcommand{\Xt}{\tilde{X}}
\newcommand{\alt}{\tilde{\alpha}}
\newcommand{\bet}{\tilde{\beta}}
\newcommand{\rht}{\tilde{\rho}}
\newcommand{\Pit}{\tilde{\Pi}}
\newcommand{\tal}{\tilde{\alpha}}
\newcommand{\tbe}{\tilde{\beta}}
\newcommand{\tPi}{\tilde{\Pi}}
\newcommand{\ab}{\ol{a}}
\newcommand{\Ab}{\ol{A}}
\newcommand{\Bb}{\ol{B}}
\newcommand{\cb}{\ol{c}}
\newcommand{\Cb}{{\ol{C}}}
\newcommand{\db}{\ol{d}}
\newcommand{\Db}{\ol{D}}
\newcommand{\eb}{\ol{e}}
\newcommand{\Eb}{\ol{E}}
\newcommand{\fb}{\ol{f}}
\newcommand{\Fb}{\ol{F}}
\newcommand{\Gb}{\ol{G}}
\newcommand{\Hb}{\ol{H}}
\newcommand{\ib}{\ol{\imath}}
\newcommand{\Ib}{\ol{I}}
\newcommand{\jb}{\ol{\jmath}}
\newcommand{\Jb}{\ol{J}}
\newcommand{\kb}{\ol{k}}
\newcommand{\Kb}{\ol{K}}
\newcommand{\nb}{\ol{n}}
\newcommand{\pb}{\ol{p}}
\newcommand{\Pb}{\ol{P}}
\newcommand{\Phib}{\ol{\Phi}}
\newcommand{\Qb}{\ol{Q}}
\newcommand{\rb}{\ol{r}}
\newcommand{\Rb}{\ol{R}}
\newcommand{\Sb}{\ol{S}}
\newcommand{\tb}{\ol{t}}
\newcommand{\Tb}{\ol{T}}
\newcommand{\Ub}{\ol{U}}
\newcommand{\Wb}{\ol{W}}
\newcommand{\xb}{\ol{x}}
\newcommand{\Xb}{\ol{X}}
\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}}
\newcommand{\vv}{\vec{v}}
\newcommand{\vw}{\vec{w}}
\newcommand{\ttab}{\{t\}}
\newcommand{\stab}{\{s\}}


\DeclareMathOperator{\Age}{Age}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\Av}{Av}
\DeclareMathOperator{\abl}{al}
\DeclareMathOperator{\asc}{asc}
\DeclareMathOperator{\BC}{BC}
\DeclareMathOperator{\capa}{cap}
\DeclareMathOperator{\codim}{codim}
\DeclareMathOperator{\ch}{ch}
%Commented out \ch for choose
\DeclareMathOperator{\col}{col}
\DeclareMathOperator{\ctt}{ct}
\DeclareMathOperator{\Der}{Der}
\DeclareMathOperator{\des}{des}
\DeclareMathOperator{\Des}{Des}
\DeclareMathOperator{\Det}{Det}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\Diag}{Diag}
\DeclareMathOperator{\diam}{diam}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\ev}{ev}
\DeclareMathOperator{\eval}{eval}
\DeclareMathOperator{\Eval}{Eval}
\DeclareMathOperator{\FPF}{FPF}
\DeclareMathOperator{\Frac}{Frac}
\DeclareMathOperator{\gen}{gen}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Harm}{Harm}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\imaj}{imaj}
\DeclareMathOperator{\inc}{inc}
\DeclareMathOperator{\Ind}{Ind}
\DeclareMathOperator{\inter}{int}
\DeclareMathOperator{\Inter}{Int}
\DeclareMathOperator{\inv}{inv}
\DeclareMathOperator{\Inv}{Inv}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\LHS}{LHS}
\DeclareMathOperator{\Mat}{Mat}
\DeclareMathOperator{\maj}{maj}
\DeclareMathOperator{\mdeg}{mdeg}
\DeclareMathOperator{\Mod}{mod}
\DeclareMathOperator{\NBB}{NBB}
\DeclareMathOperator{\nin}{nin}
\DeclareMathOperator{\Nin}{Nin}
\DeclareMathOperator{\nul}{nul}
\DeclareMathOperator{\nullity}{nullity}
\DeclareMathOperator{\NSym}{{\bf NSym}}
\DeclareMathOperator{\od}{od}
\DeclareMathOperator{\ord}{ord}
\DeclareMathOperator{\per}{per}
\DeclareMathOperator{\Pete}{Pete}
\DeclareMathOperator{\pfa}{pf}
\DeclareMathOperator{\Pm}{pm}
\DeclareMathOperator{\PM}{PM}
\DeclareMathOperator{\Pol}{Pol}
\DeclareMathOperator{\rad}{rad}
\DeclareMathOperator{\RHS}{RHS}
\DeclareMathOperator{\rk}{rk}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\reg}{reg}
\DeclareMathOperator{\rlm}{rlm}
\DeclareMathOperator{\row}{row}
\DeclareMathOperator{\sdiam}{sdiam}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\sign}{sign}
\DeclareMathOperator{\sh}{sh}
\DeclareMathOperator{\slack}{slack}
\DeclareMathOperator{\spa}{span}
\DeclareMathOperator{\st}{st}
\DeclareMathOperator{\summ}{sum}
\DeclareMathOperator{\Supp}{Supp}
\DeclareMathOperator{\sus}{susp}
\DeclareMathOperator{\Sym}{{\bf Sym}}
\DeclareMathOperator{\SYT}{SYT}
\DeclareMathOperator{\tang}{tang}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\tri}{tri}
\DeclareMathOperator{\wed}{wedge}
\DeclareMathOperator{\wt}{wt}







\newcommand{\new}[1]{\vs{5pt}\ensuremath{\blacktriangleright}#1\ensuremath{\blacktriangleleft}\vs{5pt}}
\newcommand{\bul}{\bullet}
\newcommand{\dil}{\displaystyle}
\newcommand{\dsum}{\dil\sum}
\newcommand{\dint}{\dil\int}
%\newcommand{\dfrac}{\dil\frac}
\newcommand{\scl}{\scriptstyle}
\newcommand{\ssl}{\scriptscriptstyle}
\newcommand{\foz}{\footnotesize}
\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.}
\newcommand{\caup}{Cambridge University Press}
\newcommand{\oup}{Oxford University Press} 
\newcommand{\pr}{preprint}
\newcommand{\ip}{in preparation}
\newcommand{\ds}{\displaystyle}
