\documentclass[12pt]{article}

\usepackage{fullpage}
\usepackage{amssymb}
\usepackage{amsmath}

\begin{document}

\title{LaTeX Style Guide for the\\
{\it Journal of Integer Sequences}\\
\large Version 1.19}

\date{}
\author{}
\maketitle

     Most authors of papers in {\it Journal of Integer
Sequences} prepare their papers in LaTeX.  Please observe the
following guidelines.

\section{LaTex advice}

    Please avoid the use of special-purpose macros whenever possible.
Strip your paper of references to any packages that you do not
actually use.  (Do {\it not\/} just comment them out.)

    It may be worthwhile to download the latex file for a paper already
published in the journal and model your paper on it.

    Do not include a date in your paper.

    Acknowledgments should be in a {\it separate, numbered
section} at the end of the paper.

    Please do {\it not\/} include any commands that tweak the spacing (such as
{\tt \char'134noindent}, {\tt \char'134newpage}, {\tt \char'134pagebreak},
etc.) since when your paper is formatted for final publication, the page
breaks and spacing will probably be quite different from what you currently
see.  

\section{Common Grammatical Errors}

\begin{enumerate}

\item Avoid the passive voice.  Instead of saying ``In
[1] it is shown that all primes $> 2$ are odd'', say ``Smith [1] showed
that all primes $>2$ are odd''.

\item Avoid use of weak constructions such as ``this number''.  For
example, instead of saying

Wrong:  Let $x$ be a prime.  We now square this number.

Right:  Let $x$ be a prime.  We now square $x$.

\item Avoid the use of constructions, such as ``don't'', ``can't'',
``isn't'', etc.

Wrong:  The number $7$ is prime, since it isn't divisible by
$2, 3, 4, 5, $ or $6$.  

Right:  The number $7$ is prime, since it is not divisible by
$2, 3, 4, 5, $ or $6$.

\item The word ``precise'' is not a verb in English.

Wrong:  We now precise the connection between 
$\alpha$ and $\beta$.

Right:  We now make the connection between
$\alpha$ and $\beta$ more precise.

\item Use the word ``expansion'', not ``development''.

Wrong:  Let $[a_0, a_1, \ldots]$ be the continued fraction
development of $x$.

Right:  Let $[a_0, a_1, \ldots]$ be the continued fraction
expansion of $x$.

\item Use ``associate with'', not ``associate to''.

Wrong:  We now associate $x$ to $y$.

Right:  We now associate $x$ with $y$.

\item Use ``root'' for equations, and ``zero'' for polynomials. 

Wrong:  Let $\alpha$ be the positive root of $x^2 - x - 1$.

Right:  Let $\alpha$ be the positive zero of $x^2 - x - 1$.

Right:  Let $\alpha$ be the positive root of $x^2 -x - 1 = 0$.

\item Use the term ``pair'', not ``couple'', to denote two objects.

Wrong:  Let $(\alpha, \beta)$ be a couple of real numbers.

Right:  Let $(\alpha, \beta)$ be a pair of real numbers.

\item  Always put a comma after ``i.e.'' and ``e.g.''.

Wrong:  Let $x$ be a minimal element i.e. an element such
that if $y \leq x$ then $y = x$.

Wrong:  Let $x$ be a prime e.g. $2$. 

Right:  Let $x$ be a minimal element, i.e., an element such
that if $y \leq x$ then $y = x$.

Right:  Let $x$ be a prime, e.g., $2$.

\item Avoid run-on sentences.  A run-on sentence is one that
expresses two thoughts in a single phrase.  Fix by separating
into two or more sentences, or by connecting with a semi-colon
or a conjunction such as ``and''.   More information can be found
in the Wikipedia article on run-on sentences.

Wrong:  Let $\Sigma$ be a finite alphabet, $\Sigma^*$ denote the
set of all finite words over $\Sigma$.

Right:  Let $\Sigma$ be a finite alphabet, and let
$\Sigma^*$  denote the set of all finite words over $\Sigma$.

Wrong:  Let $p$ be a prime number $\geq 3$, then $2^p \equiv 2$ (mod $p$).

Right:  Let $p$ be a prime number $\geq 3$.  Then $2^p \equiv 2$ (mod $p$).

\item Avoid starting sentences or phrases with notation.  

Wrong:  $f$ maps integers to real numbers.

Right:  The function $f$ maps integers to real numbers.

\item Avoid treating citation numbers as objects of prepositions.
Treat them syntactically like footnotes.

Wrong:  In [1] it is proved that $e$ is irrational.

Wrong:  The article [1] proves that $e$ is irrational.

Right:  Euler [1] proved that $e$ is irrational.

\item  Use colons properly.  Colons should not immediately follow
verbs.

Wrong:  The resulting equation is:
$$ x = y^2 .$$

Right:  The resulting equation is
$$ x = y^2 .$$

Right:  The resulting equation is as follows:
$$ x = y^2.$$

\item Words like ``notation'' and ``information'' are mass nouns in
English, and as such, rarely appear in the plural.   

Wrong:  We now introduce some definitions and notations.

Right:  We now introduce some definitions and notation.

The Wikipedia article on mass nouns contains more information.

\end{enumerate}



\section{Common LaTeX Errors}

     This section lists a few of the common errors made
when preparing papers in LaTeX.

\subsection{Blackboard Bold}

     For blackboard bold symbols such as
$\mathbb Z$, $\mathbb Q$, $\mathbb R$, $\mathbb C$, use
{\tt \char'134mathbb Z}, for example.  You may need to include
the command {\tt \char'134usepackage\char'173amssymb\char'175}.

\subsection{Variables}

     Usually, variables such as $x$, $y$, $n$, etc., should appear
in the italic font.  This will occur automatically if you remember
to enclose your equations (even references to a single variable) in
dollar signs or double-dollar signs, or use a latex equation environment.

\medskip

\noindent Wrong:  {\tt Let n be the number of integers in the list.}

\noindent Right:  {\tt Let \char'044 n\char'044\ be the number of integers in the list.}

\subsection{Accents}

    Be careful to use the proper accents.  The name
Erd\H{o}s, for example, uses a Hungarian accent, and
should be formatted with {\tt\char'134H}.  Create accents using
the LaTeX abbrevations; do 
{\it not\/} use UNICODE, keyboard shortcuts,
or an exotic character set to make them.

\subsection{Floor and Ceiling}

    Be sure to use the built-in \TeX\ commands
{\tt \char'134lfloor}, {\tt \char'134rfloor} and
{\tt \char'134lceil}, {\tt \char'134rceil}, not square brackets,
when using these integer functions.

\subsection{Min and Max}

     Be sure to use the built-in \TeX\ commands
{\tt \char'134min} and {\tt \char'134max} when using these functions.

\subsection{Gcd and Lcm}

     Be sure to use the built-in \TeX\ command {\tt\char'134gcd}
for greatest common divisor.  Don't write $(a,b)$ for the gcd of $a$ and
$b$; write $\gcd(a,b)$ instead.  For lcm, you will have to define
your own command so that it appears in the roman font.

\subsection{Multi-letter functions}

     As a general rule, all multi-letter functions such as $\sin, \cos, \tan,$, etc., should appear in the roman font.  For these functions you can use
the built-in \TeX\ commands {\tt\char'134sin, \char'134cos, \char'134tan}, etc.,
but for others (e.g., {\rm Li} for the logarithmic integral)
you may have to define your own commands.

\subsection{Parentheses}

      Use parentheses for grouping, not square brackets or braces.
You can get different sizes of parentheses using, for example,
{\tt \char'134bigl(} and {\tt \char'134bigr)}.

\subsection{Mod}

     Draw a distinction between the use of ``mod'' as a function of
two arguments, mapping $a \bmod b$ to the least non-negative residue
of $a$ modulo $b$, and ``mod'' as an equivalence relation.  For
the first, use the \TeX\ command {\tt\char'134bmod}.  For the second,
use the \TeX\ command {\tt\char'134pmod} for displayed equations; for
in-line equations write something like

\centerline{{\tt \char'044 x \char'134equiv a\char'044\ 
(mod \char'044b\char'044)},}

\noindent which typesets as follows: $x \equiv a$ (mod $b$).  Do not
use notation like $x \equiv y [p]$. 

\subsection{Quote marks}

     Do not enclose words in ordinary quotation
marks {\tt "like this"}.   This results in the following
ugly output:
\begin{center}
"like this"
\end{center}
Instead, use the left-quote and right-quote
symbols, {\tt ``like this''}, which gives the correct
\begin{center}
``like this'' .
\end{center}

\subsection{Proper use of {\tt\char'134ldots} and {\tt\char'134cdots}}

     Be sure to use {\tt\char'134ldots} and {\tt\char'134cdots} properly.
The rule is as follows:  you should use {\tt\char'134ldots} if the center
of mass of the items 
on either side is below the middle of the line --- for
example, if the items on either side are commas.  You should use
{\tt \char'134cdots} if the center of mass of the items on either side 
is in the middle of the line --- for example, if the items on either
side are alphabet symbols.  For example:

\medskip

Wrong:  Consider the product $a_1 a_2 \ldots a_n$.  \ \ \   (Here we used {\tt \char'134ldots}.)

Right:  Consider the product $a_1 a_2 \cdots a_n$.  \ \ \    (Here we used {\tt \char'134cdots}.)

\bigskip

Wrong:  Consider the sequence $a_1, a_2, \cdots, a_n$.  \ \ \   (Here we used {\tt \char'134cdots}.)

Right:  Consider the sequence $a_1, a_2, \ldots, a_n$.  \ \ \   (Here we used {\tt \char'134ldots}.)

\subsection{Proper punctuation of case statements}

Please punctuate case statements as follows:
\begin{displaymath}
f(x) = \begin{cases}
	1, & \text{if $x$ is irrational;} \\
	0, & \text{otherwise.}
	\end{cases}
\end{displaymath}

\section{Definitions}

Terms that are being defined should be in a special font, such as italic
or slant. 

For example,

\centerline{A {\it flern} is a 3-dimensional hypersquare.}

Avoid introducing new terms and notation when there are already accepted
equivalents widely in use in the mathematical community.
For example, for the Fibonacci numbers, you
should use the notation $F_n$, and the numbers defined by
$F_0 = 0$, $F_1 = 1$, $F_n = F_{n-1} + F_{n-2}$ for $n \geq 2$.


\section{Theorems}

Use the {\tt \char'134begin\char'173theorem\char'175} $\ldots$
and {\tt \char'134end\char'173theorem\char'175} environments for theorems,
lemmas, propositions, etc.  Theorems should be numbered.  Refer to theorems,
lemmas, propositions, sections, equations, tables etc.
using labels; do {\it not} hard-code references to them.

To get proper definitions, use the
{\tt \char'134usepackage\char'173amsthm\char'175} command.

\section{Definitions, Examples, and Remarks}

All definitions, examples, and remarks should be stated in the roman font,
except (of course) for any
mathematical symbols.  You can use the following code as an example.

\noindent{\tt \char'134theoremstyle\char'173definition\char'175} \\
\noindent{\tt \char'134newtheorem\char'173defn\char'175\char'173Definition\char'175} \\

\section{Proofs}

Use the commands {\tt \char'134begin\char'173proof\char'175} and
{\tt \char'134end\char'173proof\char'175} to delimit proofs.
These are available in the {\tt amsthm} package mentioned above.

\section{Tables}

Tables should be centered on the page, using the {\tt center}
environment.  Each table should have a number.

\section{Introduction}

Papers should have an introductory section that provides motivation and
history of the problems discussed.

\section{Abstract}

Every paper should have a short abstract of 50 to 200 words. 
The abstract should be free of symbols whenever possible, and {\it should
not\/} contain citations to the bibliography or section numbers of the
paper.  When referring to other
work in the abstract, you can refer to author's names, but avoid
mentioning years, journal names, or other information.

\section{Sequence Numbers}

Be sure to include sequence numbers from Sloane's online {\it Encyclopedia
of Integer Sequences} for all sequences you discuss in your paper.
The list of all such sequences should be summarized at the end of your
paper, sorted in ascending order.  

\section{Citations}

     Use citations syntactically like footnotes, not as objects of prepositions.
Avoid saying things like ``In [1] we find the following result.''  Instead,
say ``Jones [1] proved the following result.''  Use the LaTeX command
{\tt \char'134cite}; do {\it not\/} hard-code references to the bibliography.

      When listing citations, if the author has two initials, be sure
place a space between the two initials. 

Wrong:  N.J.A. Sloane

Right:  N. J. A. Sloane

\medskip

      Two authors should be separated with ``and'':

Wrong:  J. Smith, D. Jones

Right:  J. Smith and D. Jones

\medskip

      Three or more authors should be separated with the ``Oxford
comma''.

Wrong:  J. Smith, D. Jones and Z. Xu

Right:  J. Smith, D. Jones, and Z. Xu

\medskip

      When simultaneously citing multiple references, use syntax
similar to {\tt \char'134cite\char'173ref1,ref2,ref3\char'175} to combine
all references in a single pair of brackets; do {\it not\/} write
{\tt \char'134cite\char'173ref1\char'175, \char'134cite\char'173ref2\char'175,
\char'134cite\char'173ref3\char'175}.

      When citing a theorem or page number in another work, say
{\tt \char'134cite[p.\char'134\ 123]\char'173ref1\char'175} or something
similar.  Note in particular the backslash and space after the dot.  This is
needed because LaTeX assumes that a dot following a lowercase letter indicates
the end of a sentence, and hence inserts extra space.

     Please use the following examples when preparing citations.
Pay careful attention to punctuation and the use of roman, italic,
and bold fonts.   In particular, notice that page ranges should be separated
by two hyphens in LaTeX:  write {\tt 123--145}, not {\tt 123-145}.

Please use the standard {\it Mathematical Reviews}
abbreviations for journal names, with the exception that for particularly
obscure journals you may provide the entire name.

     The {\it Mathematical Reviews} journal abbreviation list can be
found here:

\centerline{\tt http://www.ams.org/msnhtml/serials.pdf}

\subsection{Article citation}

    1.  J. Chan and F. E. Smith, An article about Chan-Smith numbers,
    {\it J. of Chan-Smith Numbers} {\bf 13} (1998), 123--124.

Provide the volume, but {\bf not} the issue number, unless the issue
number is required to uniquely specify the paper.  Note that words in article
titles should {\it not\/} be capitalized, with the following exceptions:
the first word, proper nouns, and German nouns.    The journal name should
be in italics; the volume number should be in bold.  Do not use ``pp.'' to
provide page numbers for articles.

\subsection{Book citation}

    2.  A. Alces, {\it Introduction to Moose Theory}, Springer, 1995.

Book titles should be in italics.
Note that words in book titles should be capitalized, with the exception of
very short unimportant words, such as ``to'', ``of'', ``and'', etc.
Do not include the ISBN number.  It is not necessary to give the place
of publication unless it is a very rare or hard-to-find book.

\subsection{Article in Conference Proceedings or Book}

    3.  B. Franklin, The public library as an aid to research,
    in G. Washington and T. Jefferson, eds., {\it Public Libraries in
    the United States}, Addison-Wesley, 2001, pp.\ 16--32.

Capitalize the name of the book, but {\it not\/} the paper you are referring to
in the book.  Note that here, unlike the case of a journal article, the
abbreviation ``pp.'' is used.

\subsection{Unpublished Material or Material on the Web}

     4.  B. Obama, G. Bush, and W. J. Clinton,
     Combinatorial reasoning in American elections,
	 preprint,  {\tt http://www.barackobama.com/combin.pdf}.


\section{Other Issues}

All sections of your paper should be numbered.  Do not hard-code references
to section numbers.

Please be sure that your paper contains a list of {\it key words
and phrases} and the appropriate
{\it 2000 Mathematics Subject Classifications}.  (A list of all these
classifications can be found at
{\tt http://www.ams.org/msnhtml/classification.pdf}.)

Avoid starting a line of your file  with the word ``From''.  Many mailers
insert a $>$ character in such lines, causing a question mark to appear
in your text.  If you must start a line of the file with the
word ``From'', you can insert a space first.


\end{document}
