>From: Arturo Carpi <arturo@arturo.cib.na.cnr.it>
Date: Wed, 24 Mar 1999 12:28:55 +0100
To: guoniu@math.u-strasbg.fr
Subject: SLC 42

Dear colleague,

I uploaded the revised version of a paper for SLC 42 to
  ftp://cartan.u-strasbg.fr/pub/slc/incoming
Find please below the technical details and the abstract.

I would greately appreciate to know whether the paper was received and 
succesfully compiled.

Thanks in advance

Arturo Carpi

-----


1) Technical aspect

Author's name and email address :
  Arturo Carpi - arturo@arturo.cib.na.cnr.it
  Aldo de Luca - deluca@mercurio.mat.uniroma1.it

Name of file uploaded :
  repeatedFactors.tex

File type :
  mathpaper

Size of file in KBytes :
  64

Date of uploading :
  March 24, 1999

Compression format :
  none

Hardware and software required :

Text format (if text) :
  LaTeX2e (Written under MacOS)

2) Description of the document

  Revised version of the paper 'Words and Repeated Factors'
  for SLC 42.

3) An abstract

In this paper we consider sets of factors of a finite word which permit us to 
reconstruct the entire word.  This analysis is based on the notion of box.  The 
initial (resp. terminal) box of  w  is the shortest prefix (resp. suffix) of  w  
which is an unrepeated factor.  A factor  u  of  w  is a proper box if there 
are letters  a,  a',  b,  b',  with  a'  different from  a  and  b'  different 
from  b,  such that  u = asb  and  a's,  sb'  are factors of  w.  A box is 
called maximal if it is not a proper factor of another box.  The main result of 
the paper is the following theorem (maximal box theorem):  Any finite word  w  
is uniquely determined by the initial box, the terminal box and the set of 
maximal boxes.  Another important combinatorial notion is that of superbox.  A 
superbox is any factor of  w  of the kind  asb,  with  a,  b  letters, such 
that  s  is a repeated factor, whereas  as  and  sb  are unrepeated factors.  A 
theorem for superboxes similar to the maximal box theorem is proved.  Some 
algorithms allowing us to construct boxes and superboxes and, conversely, to 
reconstruct the word are given.  An extension of these results to languages is 
also presented.




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Arturo Carpi                 via Toiano, 6              phone: +39(81)8534225
Istituto di Cibernetica      80072 Arco Felice (NA)     fax  : +39(81)5267654
CNR                          ITALY
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