Infinite permutations of lowest maximal pattern complexity
Combinatorics
2009-11-09 v2
Abstract
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and words. In this paper, we define maximal pattern complexity for infinite permutations and show that this complexity function is ultimately constant if and only if the permutation is ultimately periodic. Then we characterize the non-periodic permutations of minimal complexity (equal to n) and find that they all are constructed with the use of Sturmian words.
Keywords
Cite
@article{arxiv.0910.5696,
title = {Infinite permutations of lowest maximal pattern complexity},
author = {S. V. Avgustinovich and A. E. Frid and T. Kamae and P. V. Salimov},
journal= {arXiv preprint arXiv:0910.5696},
year = {2009}
}
Comments
Announced at WORDS 2009 in Salerno, to be submitted to the special issue of TCS