Idempotent Rank of the Transformations Semigroup with Palindromic Image
Abstract
Let $X_n=\{1,2,\ldots,n\}$, and denote by $P_n$ the semigroup of all palindromic transformations on $X_n$. In this paper, we derive an explicit formula for the number of idempotent elements in $P_n$. Furthermore, we prove that $P_n$ is not generated by its idempotents for $n\ge 3$, concluding that its idempotent rank is undefined.
Keywords
References
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