From toufik@math.haifa.ac.il Thu Apr 7 03:16:44 2005 Return-Path: Received: from math.haifa.ac.il (math.haifa.ac.il [132.74.112.24]) by graceland.math.uwaterloo.ca (8.11.7/8.11.7) with ESMTP id j377GFH27654 for ; Thu, 7 Apr 2005 03:16:16 -0400 (EDT) Received: by math.haifa.ac.il (Postfix, from userid 16014) id B5E591C4348; Thu, 7 Apr 2005 09:33:53 +0300 (IDT) Received: from localhost (localhost [127.0.0.1]) by math.haifa.ac.il (Postfix) with ESMTP id 680A2248300 for ; Thu, 7 Apr 2005 09:33:52 +0300 (IDT) Date: Thu, 7 Apr 2005 09:33:52 +0300 (IDT) From: Toufik Mansour To: Jeffrey Shallit Subject: Re: Submission to the Journal of Integer Sequences In-Reply-To: <200504051424.j35EOmN17948@graceland.math.uwaterloo.ca> Message-ID: References: <200504051424.j35EOmN17948@graceland.math.uwaterloo.ca> MIME-Version: 1.0 Content-Type: MULTIPART/MIXED; BOUNDARY="1250170992-1694740403-1112855632=:21875" X-Greylist: Delayed for 00:50:34 by milter-greylist-1.6 (graceland.math.uwaterloo.ca [129.97.75.152]); Thu, 07 Apr 2005 03:16:43 -0400 (EDT) Status: RO This message is in MIME format. The first part should be readable text, while the remaining parts are likely unreadable without MIME-aware tools. Send mail to mime@docserver.cac.washington.edu for more info. --1250170992-1694740403-1112855632=:21875 Content-Type: TEXT/PLAIN; charset=US-ASCII Dear Professor Jeffrey Shallit, First, Thanks a lot. Here it is the tex file of the paper with all its figures and the pdf, dvi, and ps files. If there any thing missing or any question, then please feel free to contact me. >-------------------------------------------------------< >All the best < >Toufik Mansour < > < >Department of Mathematics, Haifa University < >31905 Haifa, Israel < > < >Email: toufik@math.haifa.ac.il, tmansur11@hotmail.com < >URL : math.haifa.ac.il/toufik < >-------------------------------------------------------< On Tue, 5 Apr 2005, Jeffrey Shallit wrote: > Dear Toufik Mansour: > > I have now received the referee's report on your paper, > "Pattern Avoidance in Matrices", > and it is attached below. > > As you can see the referee likes your paper and believes it > should be accepted, but has a number of minor suggestions > to improve the paper. > > Please revise your paper in accordance with the referee's > suggestions and send me a new version. > > Please BE SURE your paper conforms to the Journal's latex > style guidelines, available on the Journal's home page. > Non-conforming papers CANNOT be published. > > Thank you for considering the Journal of Integer Sequences. > > Jeffrey Shallit > Editor-in-Chief > Journal of Integer Sequences > > --------------------------- cut here for latex report ---------------- > > \documentclass[11pt]{article} > > \textwidth 6.5in > \textheight 9in > \oddsidemargin 0.0in > \topmargin -0.5in > \parskip 0.1in > > \usepackage{amsmath,amssymb,amsfonts} > > \begin{document} > > \title{ > Referee's Report on\\ > \emph{Pattern Avoidance in Matrices}\\ > by Sergey Kitaev, Toufik Mansour and Antoine Vella} > > \maketitle > > \thispagestyle{empty} > > The authors generalize the concept of pattern avoidance from words > to matrices. They establish a connection between pattern avoidance > on matrices and bipartite Ramsey-type problems as well as enumerate > $(0,1)$-matrices avoiding certain small $(0,1)$-patterns of up to 4 > entries, obtaining generating functions either by direct > combinatorial argument or using the transfer matrix method. > > These results and the direction this paper takes in the study of > restricted permutations are interesting, and my recommendation is > for this paper to be accepted with only minor corrections listed > below. > > \begin{itemize} > > \item Substance: > > \begin{enumerate} > > \item Page 2, paragraph 1, last line: ``\dots451428 is an occurrence of > 683659\dots'' It is common in the pattern-avoidance literature to > denote a pattern of a word by reducing it to an alphabet > $\{1,\dots,k\}$ for the smallest possible $k$. Thus, in this case, I > would write ``\dots451428 is an occurrence of 341325\dots''. > > \item Pages 9--12: The proof of Proposition 3, although correct, is > too long. It may be shortened thus: > > Let $A$ be an $m\times n$ matrix avoiding the pattern > {$\pi=\tiny\begin{matrix}\fbox{0}&\!\!\!\!\!\!\!\!\fbox{1}\\\fbox{1}&\!\!\!\!\!\!\!\!~\end{matrix}$}. > Clearly, an empty matrix avoids $\pi$, so $c_{m,0}=c_{0,n}=1$. > Suppose that $A$ is a matrix of size $m\times n$ with $m,n\ge 1$. > > If the top row of $A$ contains only zeros, then it does not affect > the rest of the matrix and can be removed to obtain a $\pi$-avoiding > matrix of $m-1$ rows and $n$ columns. Now suppose the top row of $A$ > contains a 1. Suppose that in the top row there are $i$ zeros to > left of the rightmost 1. Since $A$ avoids $\pi$, the $i$ columns > containing those top zeros must be zero columns. Thus, these columns > cannot be involved in an occurrence of $\pi$, so they may be > removed. The resulting top row has all 1s to the left of all 0s, so > this top row cannot be involved in an occurrence of $\pi$, and > hence, may be removed as well. Each choice of $i+1$ positions (those > of the rightmost 1 in the top row and $i$ zeros to its left) yields, > after the two removals, an $(m-1)\times(n-i)$ matrix avoiding $\pi$. > Thus, > \[ > c_{m,n}=c_{m-1,n}+\sum_{i=0}^{n-1}{\binom{n}{i+1}c_{m-1,n-i}}, \quad > m,n\ge 1. > \] > Straightforward technical manipulations, which are omitted, now > yield the recursive formula for $a(x,y)=\mathrm{ogf}\{c_{m,n}\}$ at > the end of the proof of Proposition 3. > > \end{enumerate} > > \item Typos: > > \begin{enumerate} > > \item Page 11, line 4: $\binom{k}{i}$ should be $\binom{j}{i}$. > > \item Page 12, line 8 (last formula in section 2.2): at the end of > the denominator of the first fraction, the right parenthesis is > omitted. The correct denominator is $(1-y)(x+(1-x)y)$. > > \item Page 18, line $-7$: ``$m=2$'' should be ``$m=3$''. > > \item Page 18, line $-3$: ``$m$'' should be ``$m=2$''. > > \item Pages 20-21, parts (i) of Corollaries 12, 13, 14: the exponent > in the right-hand side should be ``$n-1$'', not ``$n-3$''. > > \end{enumerate} > > \end{itemize} > > \end{document} > --1250170992-1694740403-1112855632=:21875 Content-Type: APPLICATION/postscript; name="1201.ps" Content-Transfer-Encoding: BASE64 Content-ID: Content-Description: Content-Disposition: attachment; filename="1201.ps" JSFQUy1BZG9iZS0yLjAKJSVUaXRsZTogMTIwMS5wcwolJUNyZWF0b3I6IGZp ZzJkZXYgVmVyc2lvbiAzLjIgUGF0Y2hsZXZlbCAxCiUlQ3JlYXRpb25EYXRl OiBGcmkgTWFyIDE5IDE5OjI4OjM0IDIwMDQKJSVGb3I6IGF2ZWxsYUBiZXRh Lm1hdGggKEFudG9pbmUgVmVsbGEsTUM1MTYxLHg2NDEwLDg4Ni04NDk3LDU3 IERpZXR6IEF2ZS4gU291dGgsIFdhdGVybG9vKQolJU9yaWVudGF0aW9uOiBM YW5kc2NhcGUKJSVCb3VuZGluZ0JveDogODkgMjMzIDUyMyA1NTkKJSVQYWdl czogMQolJUJlZ2luU2V0dXAKJSVJbmNsdWRlRmVhdHVyZTogKlBhZ2VTaXpl 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