Derives an explicit formula for idempotent elements in palindromic transformations semigroup, indicating its undefined rank for larger n.
Let Xₙ=\1,2,…,n\, and denote by Pₙ the semigroup of all palindromic transformations on Xₙ. In this paper, we derive an explicit formula for the number of idempotent elements in Pₙ. Furthermore, we prove that Pₙ is not generated by its idempotents for n≥ 3, concluding that its idempotent rank is undefined.
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Osman Kelekci̇ (2026) studied this question.
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