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\begin{document}

\title[DIMACS Sample]{DIMACS Book Series Sample}

%    Information for first author
\author{Author One}
%    Address of record for the research reported here
\address{Department of Mathematics, Louisiana State University, Baton
Rouge, Louisiana 70803}
%    Current address
\curraddr{Department of Mathematics and Statistics,
Case Western Reserve University, Cleveland, Ohio 43403}
\email{xyz@math.university.edu}
%    \thanks will become a 1st page footnote.
\thanks{The first author was supported in part by NSF Grant \#000000.}

%    Information for second author
\author{Author Two}
\address{Mathematical Research Section, School of Mathematical Sciences,
Australian National University, Canberra ACT 2601, Australia}
\email{two@maths.univ.edu.au}
\thanks{Support information for the second author.}

%    General info
\subjclass[2000]{Primary 54C40, 14E20; Secondary 46E25, 20C20}
\date{January 1, 1994 and, in revised form, June 22, 1994.}

\dedicatory{This paper is dedicated to our advisors.}

\keywords{Differential geometry, algebraic geometry}

\copyrightinfo{2003}{American Mathematical Society}

\begin{abstract}
This paper is a sample prepared to illustrate the use of the American Mathematical Society's \LaTeX{} document
class \texttt{dimacs-l}. Please be sure to read Section 3. It contains instructions for authors that apply
specifically to volumes in the DIMACS series. Volume 61 of the DIMACS book series (Bioconsensus) is an example of
a volume prepared using the guidelines contained herein.
\end{abstract}

\maketitle


\section*{This is an unnumbered first-level section head}
This is an example of an unnumbered first-level heading.

\specialsection*{This is a special section head}
This is an example of a special section head%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\footnote{Here is an example of a footnote. Notice that this footnote
text is running on so that it can stand as an example of how a footnote
with separate paragraphs should be written.
\par
And here is the beginning of the second paragraph.}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
.

\section{This is a numbered first-level section head}
This is an example of a numbered first-level heading.

\subsection{This is a numbered second-level section head}
This is an example of a numbered second-level heading.

\subsection*{This is an unnumbered second-level section head}
This is an example of an unnumbered second-level heading.

\subsubsection{This is a numbered third-level section head}
This is an example of a numbered third-level heading.

\subsubsection*{This is an unnumbered third-level section head}
This is an example of an unnumbered third-level heading.

\begin{lemma}
Let $f, g\in  A(X)$ and let $E$, $F$ be cozero
sets in $X$.
\begin{enumerate}
\item If $f$ is $E$-regular and $F\subseteq E$, then $f$ is $F$-regular.

\item If $f$ is $E$-regular and $F$-regular, then $f$ is $E\cup
F$-regular.

\item If $f(x)\ge c>0$ for all $x\in E$, then $f$ is $E$-regular.

\end{enumerate}
\end{lemma}

The following is an example of a proof. It uses the
\begin{verbatim}
\begin{proof}, \end{proof} environment.
\end{verbatim}
\begin{proof} Set $j(\nu)=\max(I\backslash a(\nu))-1$. Then we have
\[
\sum_{i\notin a(\nu)}t_i\sim t_{j(\nu)+1}
  =\prod^{j(\nu)}_{j=0}(t_{j+1}/t_j).
\]
Hence we have
\begin{equation}
\begin{split}
\prod_\nu\biggl(\sum_{i\notin
  a(\nu)}t_i\biggr)^{\abs{a(\nu-1)}-\abs{a(\nu)}}
&\sim\prod_\nu\prod^{j(\nu)}_{j=0}
  (t_{j+1}/t_j)^{\abs{a(\nu-1)}-\abs{a(\nu)}}\\
&=\prod_{j\ge 0}(t_{j+1}/t_j)^{
  \sum_{j(\nu)\ge j}(\abs{a(\nu-1)}-\abs{a(\nu)})}.
\end{split}
\end{equation}
By definition, we have $a(\nu(j))\supset c(j)$. Hence, $\abs{c(j)}=n-j$
implies (5.4). If $c(j)\notin a$, $a(\nu(j))c(j)$ and hence
we have (5.5).
\end{proof}

\begin{quotation}
This is an example of an `extract'. The magnetization $M_0$ of the Ising
model is related to the local state probability $P(a):M_0=P(1)-P(-1)$.
The equivalences are shown in Table~\ref{eqtable}.
\end{quotation}

\begin{table}[ht]
\caption{}\label{eqtable}
\renewcommand\arraystretch{1.5}
\noindent\[
\begin{array}{|c|c|c|}
\hline
&{-\infty}&{+\infty}\\
\hline
{f_+(x,k)}&e^{\sqrt{-1}kx}+s_{12}(k)e^{-\sqrt{-1}kx}&s_{11}(k)e^
{\sqrt{-1}kx}\\
\hline
{f_-(x,k)}&s_{22}(k)e^{-\sqrt{-1}kx}&e^{-\sqrt{-1}kx}+s_{21}(k)e^{\sqrt
{-1}kx}\\
\hline
\end{array}
\]
\end{table}

\begin{definition}
This is an example of a `definition' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{definition}

\begin{remark}
This is an example of a `remark' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{remark}

\begin{example}
This is an example of an `example' element.
For $f\in A(X)$, we define
\begin{equation}
\mathcal{Z} (f)=\{E\in Z[X]: \text{$f$ is $E^c$-regular}\}.
\end{equation}
\end{example}

\begin{xca}
This is an example of the \texttt{xca} environment. This environment is
used for exercises which occur within a section.
\end{xca}

The following is an example of a numbered list.

\begin{enumerate}
\item First item.
In the case where in $G$ there is a sequence of subgroups
\[
G = G_0, G_1, G_2, \dots, G_k = e
\]
such that each is an invariant subgroup of $G_i$.

\item Second item.
Its action on an arbitrary element $X = \lambda^\alpha X_\alpha$ has the
form
\begin{equation}\label{eq:action}
[e^\alpha X_\alpha, X] = e^\alpha \lambda^\beta
[X_\alpha X_\beta] = e^\alpha c^\gamma_{\alpha \beta}
 \lambda^\beta X_\gamma,
\end{equation}

\begin{enumerate}
\item First subitem.
\[
- 2\psi_2(e) =  c_{\alpha \gamma}^\delta c_{\beta \delta}^\gamma
e^\alpha e^\beta.
\]

\item Second subitem.
\begin{enumerate}
\item First subsubitem.
In the case where in $G$ there is a sequence of subgroups
\[
G = G_0, G_1, G_2, \ldots, G_k = e
\]
such that each subgroup $G_{i+1}$ is an invariant subgroup of $G_i$ and
each quotient group $G_{i+1}/G_{i}$ is abelian, the group $G$ is called
\textit{solvable}.

\item Second subsubitem.
\end{enumerate}
\item Third subitem.
\end{enumerate}
\item Third item.
\end{enumerate}

Here is an example of a cite. See \cite{Arro:63}.

\begin{theorem}
This is an example of a theorem.
\end{theorem}

\begin{theorem}[Marcus Theorem]
This is an example of a theorem with a parenthetical note in the
heading.
\end{theorem}

\begin{figure}[tb]
\blankbox{.6\columnwidth}{5pc}
\caption{This is an example of a figure caption with text.}
\label{firstfig}
\end{figure}

\begin{figure}[tb]
\blankbox{.75\columnwidth}{3pc}
\caption{}\label{otherfig}
\end{figure}

\section{Some more list types}
This is an example of a bulleted list.

\begin{itemize}
\item $\mathcal{J}_g$ of dimension $3g-3$;
\item $\mathcal{E}^2_g=\{$Pryms of double covers of $C=\openbox$ with
normalization of $C$ hyperelliptic of genus $g-1\}$ of dimension $2g$;
\item $\mathcal{E}^2_{1,g-1}=\{$Pryms of double covers of
$C=\openbox^H_{P^1}$ with $H$ hyperelliptic of genus $g-2\}$ of
dimension $2g-1$;
\item $\mathcal{P}^2_{t,g-t}$ for $2\le t\le g/2=\{$Pryms of double
covers of $C=\openbox^{C'}_{C''}$ with $g(C')=t-1$ and $g(C'')=g-t-1\}$
of dimension $3g-4$.
\end{itemize}

This is an example of a `description' list.

\begin{description}
\item[Zero case] $\rho(\Phi) = \{0\}$.

\item[Rational case] $\rho(\Phi) \ne \{0\}$ and $\rho(\Phi)$ is
contained in a line through $0$ with rational slope.

\item[Irrational case] $\rho(\Phi) \ne \{0\}$ and $\rho(\Phi)$ is
contained in a line through $0$ with irrational slope.
\end{description}

\section{Special instructions from DIMACS}
\noindent
Here are some additional instructions from DIMACS. They are issued in
the hope that the volumes in this series will have a uniform
appearance. DIMACS can if requested provide help to authors who are not familiar with latex.

The American Mathematical Society has a number of files designed to aid authors of papers
destined for volumes in the DIMACS series. They can be found on the following web page:

\medskip
\begin{verbatim}
             http://www.ams.org/tex/author-info.html
\end{verbatim}

\medskip
\noindent
Just click on the line designated for DIMACS volumes. But you should ignore the sample article
you will find there. It has been supplanted by the article you are reading.

\medskip \noindent
\textbf{General considerations:}

Please use a 10 point font. This is the default font.

AMS provides a special command for absolute values.

Figures should be cited in the form  Figure \ref{firstfig},
tables as Table \ref{eqtable}.

Captions for tables should appear at the top of the table. Captions
for figures at the bottom.

Please use the
\begin{verbatim}
\begin{proof}, \end{proof} environment.
\end{verbatim}

Sections should be numbered. Only the first word of a section title
should be capitalized. There are obvious exceptions involving
proper names.

The ``thanks'' command  on the first page should be used only
to acknowledge grant
support. Any other acknowledgments belong at the end of the paper
in a section labelled Acknowledgments. This section should \emph{not} be
numbered. The proper command is
\begin{verbatim}
     \section*{Acknowledgements}.
\end{verbatim}

\noindent
The command
\begin{verbatim}
   \title[short title]{longer title}
\end{verbatim}
will make the short title the running head, and the longer title
the real title of your paper

\medskip
Please use the 2000 Math Subject Classification, and show the
Copyright information as 20xx American Mathematical Society, where
20xx is the appropriate year.  Also,
please specify style {A} for the bibliography.
These commands take the format

\begin{verbatim}
  \copyrightinfo{20xx}{American Mathematical Society}
  \subjclass[2000]{. . .}
  \begin{thebibliography}{A}
\end{verbatim}

The subject classifications should just include the code numbers (like
06A15) and not the text description of the code.

The term ``et al.'' is an abbreviation from Latin. Despite this, it
should NOT be in italics (See the Chicago Style Manual). To indicate
Harold Johnson and other authprs, you would write Harold Johnson et al.
with no punctuation before the ``et''.

If a colon separates a phrase from a sentence, the first word
after the colon does not get capitalized. If it separates two sentences,
the first word after the colon is capitalized.
%\newpage

\medskip
\noindent
\textbf{Citations:}

\medskip
There are two acceptable forms for citations. The proper style for
your article depends upon the style decision made by the editor(s) of
your volume. Citations should be listed alphabetically by the first
author's last name. Style 1 would cite by reference number. Multiple
citations should be in numerical order (e.g., see [6] and [9], rather
than see [9] and [6]). Also, a citation like ``for trees [2]'' is
correct, while ``for trees ([2])'' is not. On the other hand, saying
``for trees (see [2], p.~198) is acceptable.

Style 2 would cite by a sequence of capital letters, as in
\cite{sample2}. Sample formats are provided in the bibliography.

\medskip
Here is an itemized list of some picky things involving citations.

\begin{enumerate}
\item In the bibliography, the numbers should be enclosed in square
brackets, as in [23] for reference 23. If you use the suggested
command to create the bibliography, this is the default.
\item Names of journals should either be spelled out in full, or the approved
abbreviation from Math.~Reviews used. Please be consistent. If a journal is
abbreviated in one citation in your paper, it should be abbreviated in all
citations. Journal names are to be in italics. You can abbreviate some journal
titles and not others, as long as you are consistent.
\item The references appearing in the bibliography at the end of this
document provide the style guide.

\item Titles of articles are not in italics. This applies to both
journal articles and articles appearing in books.
\item Book titles are in italics. All words are capitalized except for
connectives  like and, but, etc. (See \cite{Arro:63}).
\item Publishers should not be abbreviated. The format follows:
American Mathematical Society, Providence, 1993.
\item Only the first word in a title of a paper gets a capital in
a citation.
\item Journal citations have a different format for indicating year of
publication. See \cite{Adam:72} in the bibliography.
\item Two authors are indicated as I. Smart and G. Bush, while three
or more authors are indicated with an extra comma as I. Smart, G.~Bush,
and S. Spade as in \cite{CJPo:94}.
\item First names of authors should be indicated as they appear in the
reference you are citing. Again be consistent. If you use B. Leclerc
in one citation, you should use it in all citations.
Hyphenations should be preserved. Thus Jean-Claude would be
abbreviated to J.-C.
\item Each citation should include names of all authors. Please
do not use shorthand like \bysame to denote repeats.
\item Do not use the symbol $\&$ to denote the word ``and''.

\item For a paper that appears as part of a volume: see the bibliography
for guidelines. Examples are provided by \cite{BLec:95} and \cite{BMP}.
\item Doctoral Dissertations \cite{benj} are treated as if they were books.
Technical reports \cite{RFish} are also treated as if they were
books.
\item Personal communicaations can be referred to simply in the format
author, personal communication, date.
\item Papers appearing in the current volume are cited as in
\cite{lap}.

\end{enumerate}


\medskip
%\bibliographystyle{amsalpha}

\begin{thebibliography}{A}

\bibitem{Adam:72} E. N. Adams III,
  Consensus techniques and the comparison of taxonomic trees,
  \emph{Systematic Zoology} \textbf{21} (1972), 390--397.

\bibitem{Adam:86} E. N. Adams III,
  $n$-Trees as nestings: complexity, similarity, and consensus,
  \emph{Journal of Classification} \textbf{3} (1986), 299--317.

\bibitem{Arro:63} K. J. Arrow,
  \emph{Social Choice and Individual Values}, second ed.,
  John Wiley, New York, 1970.

\bibitem{BLec:95} J.--P. Barth\'{e}lemy and B. Leclerc,
  The median procedure for partitions,
  in (I. J. Cox, P. Hansen, and B. Julesz, eds.),
  \emph{Partitioning Data Sets},
  American Mathematical Society, Providence, 1995, 3--34.

\bibitem{BMP} J.--P.\ Barth\'{e}lemy, F. R. McMorris, and
  R. C. Powers,
  Independence conditions for consensus $n$-trees revisited,
  \emph{Appl.~Math.~Lett.}\textbf{4} (1991), 43--46.

\bibitem{benj} R. Cramer-Benjamin, \emph{Independence in the Ordinal Model
   and on Closed Set Systems}, Doctoral dissertation, University of
   Massachusetts, Amherst, 1998.

\bibitem{CJPo:94} G. D. Crown, M. F. Janowitz, and R. C. Powers,
  An ordered set approach to neutral consensus functions,
  in (E. Diday, Y. Lechevallier, M. Schader, P. Bertrand,
  and B. Burtschy, eds.),
  \emph{New Approaches in Classification and Data Analysis},
  Springer-Verlag, Berlin, 1994, 102--110.

\bibitem{RFish} P. C. Fishburn and F. S. Roberts, \emph{Minimal Forbidden
Graphs for $L(2,1)$-Colorings}, DIMACS Technical Report 2000-32, Rutgers,
Piscataway, 2000.

\bibitem{lap} F.-J. Lapointe and G. Cucumel, How good can a consensus
get? Assessing the reliability of consnensus trees in phylogenetic
studies, this volume.

\bibitem[HKT6]{sample2} sample of style 2 citation
\end{thebibliography}
\end{document}