  I am going to compare well-known properties of infinite words with those of
infinite permutations, a new object studied since middle 2000s. Basically, it
was Sergey Avgustinovich who invented this notion, although in an early study
by Davis et al. permutations appear in a very similar framework as early as in
1977. I am going to tell about periodicity of permutations, their complexity
according to several definitions and their automatic properties, that is, about
usual parameters of words, now extended to permutations and behaving sometimes
similarly to those for words, sometimes not. Another series of results concerns
permutations generated by infinite words and their properties. Although this
direction of research is young, many people, including two other speakers of
this meeting, have participated in it, and I believe that several more topics
for further study are really promising.
