A generalization of the slice-ribbon conjecture for two-bridge knots and $t_n$-move

Daemi and Scaduto gave an extension of the slice-ribbon conjecture which asks whether a smooth concordance between a knot and a torus knot induces a ribbon concordance between them with an appropriate direction. In this paper, we characterize the two-bridge knots smoothly concordant to non-trivial torus knots via a local move called $t_n$-move. As an application, we confirm that Daemi and Scaduto's extension of the slice-ribbon conjecture is true for all two-bridge knots.