Abstract
ABSTRACT Let 𝒫 𝒞 n be the semigroup of all decreasing and order-preserving partial transformations of an n-element chain, and let E(𝒫 𝒞 n ) be its set of idempotents. Among other results, asymptotic formulae for |𝒫 𝒞 n | and |E(𝒫 𝒞 n )|/|𝒫 𝒞 n | are obtained. Similar results for 𝒫 𝒪 n the (larger) semigroup of all order-preserving partial transformations of an n-element chain are also obtained.
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