Virtualized n-gon moves for virtual knots and links

We introduce a local deformation called the virtualized [Formula: see text]-gon move for virtual knots and links ([Formula: see text]), inspired by virtualized [Formula: see text]-move introduced by [T. Nakamura, Y. Nakanishi, S. Satoh and K. Wada, Virtualized Delta moves for virtual knots and links, preprint (2024), arXiv:2401.12506]. We show that the virtualized [Formula: see text]-gon move is an unknotting operation for virtual knots for any [Formula: see text], and give a necessary and sufficient condition for two virtial links to be related by a finite sequence of virtualized [Formula: see text]-gon moves.