  In [X. Droubay et al, Episturmian words and some constructions of de Luca and
Rauzy, Theoret. Comput. Sci. 255 (2001)], it was proved that every word w has
at most |w|+1 many distinct palindromic factors, including the empty word. The
unified study of words which achieve this limit was initiated in [A. Glen et
al, Palindromic richness, Eur. Jour. of Comb. 30 (2009)]. They called these
words rich (in palindromes).
  This article contains several results about rich words and especially
extending them. We say that a rich word w can be extended richly with a word u
if wu is rich. Some notions are also made about the infinite defect of a word,
the number of rich words of length n and two-dimensional rich words.

Combinatorics