Abstract
We classify cross-sections of the ℒ and ℛ Green's relations on the finite symmetric inverse semigroup ℐ𝒮 n , determine which of them are isomorphic, and study their disposition with respect to the ℋ-cross-sections of ℐ𝒮 n .
Acknowledgments
This paper was written during the visit of the first author to Uppsala University, which was supported by The Royal Swedish Academy of Sciences. The financial support of The Academy and the hospitality of Uppsala University are gratefully acknowledged. For the second author the research was partially supported by The Swedish Research Council. We are also thankful to the referee for many helpful suggestions that led to the improvements in the paper.