Bispecial and separator factors in the generalized Thue-Morse word

Abstract

In this paper, we study some combinatorics properties of the generalized Thue-Morse word t_q generated by the morphism: μ_q(k) = k(k + 1)(k + 2). . .(k + q - 1), where k    {0, 1, . . . , q -1}, q  2 and the letters k are expressed modulo q. We focus our study on the bispecial factors in these sequences. More precisely, we describe bispecial biprolongable and bispecial q-prolongable factors and we show that they are the only bispecial factors in t_q. We end by the complete description of the separator factors.

Keywords: Infinite word; Biprolongable bispecial factors; q-prolongable bispecial factors; Separator factors.

2020 Mathematics Subject Classification: 11B85, 03D15, 68R15