Kelekci, Osman2024-11-072024-11-0720201310-1331https://doi.org/10.7546/CRABS.2020.06.01https://hdl.handle.net/11480/14904Let T-n, S-n, and STn = T-n \ S-n denote the full transformations semi-group, the symmetric group, and the singular transformations semigroup of {1, 2, . . ., n}, respectively. We define palindromic transformations in T-n as transformations with palindromic images. The set P-n of all palindromic transformations forms a subsemigroup of T-n, for each n >= 2. The aim of this paper is to give the left relative rank of the semigroup P-n with respect to the symmetric group S-n. As a consequence, we obtain the left relative rank of T-n with respect to S-n. Additionally, we compute the generating function of the sequence of numbers of the left relative ranks of P-n with respect to S-n.eninfo:eu-repo/semantics/closedAccesstransformationpalindromeidempotentrankArticle73675175710.7546/CRABS.2020.06.012-s2.0-85109006039Q3WOS:000546728400001Q4