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On infinite permutations

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 non-periodic permutations. Its answer is different for the right infinite and the bi-infinite case.
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Dmitri G. Fon-Der-Flaass, Anna E. Frid. On infinite permutations. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.267-272, ⟨10.46298/dmtcs.3458⟩. ⟨hal-01184447⟩



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