Combinatorics on Words 10th International Conference WORDS 2015
نویسندگان
چکیده
This paper defines and studies the notion of primitive root of a bi-periodic infinite picture, that is a rectangular pattern that tiles the bi-periodic picture and contains exactly one representative of each equivalence class of its pixels. This notion extends to dimension 2 the notion of primitive root of a bi-infinite periodic word. We prove that, for each bi-periodic infinite picture P, Ź there exists at least one primitive root of P; Ź there are at most two ordered pairs of positive integers (m, n) such that every primitive root of P has size mˆ n; Ź for each such pair (m, n), every rectangular pattern of size mˆ n extracted from P is a primitive root of P. We also discuss some additional properties of primitive roots.
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Pakistan International Biennial Conference on “Ramadan and Health”-10th & 11th October 2015.
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تاریخ انتشار 2015