2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 267272
author:  Dmitri G. FonDerFlaass and Anna E. Frid 

title:  On infinite permutations 
keywords:  infinite permutation, ordering, periodicity, complexity, subword complexity, Sturmian words 
abstract: 
We define an infinite permutation as a sequence of reals
taken up to the order, or, equivalently, as a linear
ordering of a finite or countable set. Then we introduce
and characterize periodic permutations; surprisingly, for
each period
t
there is an infinite number of distinct
t
periodic permutations. At last, we introduce a
complexity notion for permutations analogous to subword
complexity for words, and consider the problem of minimal
complexity of nonperiodic permutations. Its answer is
different for the right infinite and the biinfinite case.

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reference:  Dmitri G. FonDerFlaass and Anna E. Frid (2005), On infinite permutations, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 267272 
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