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Asymptotic Results for Semigroups of Order-Preserving Partial Transformations |
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| Authors: | A Laradji |
| Institution: | Department of Mathematical Sciences , KFUPM , Dhahran, Saudi Arabia |
| Abstract: | Let 𝒫 n be the semigroup of all decreasing and order-preserving partial transformations of an n-element chain, and let E(𝒫 n ) be its set of idempotents. Among other results, asymptotic formulae for |𝒫 n | and |E(𝒫 n )|/|𝒫 n | are obtained. Similar results for 𝒫 n the (larger) semigroup of all order-preserving partial transformations of an n-element chain are also obtained. |
| Keywords: | Double/small Schröder number Generating function Idempotents Integral representation Legendre polynomial Order-decreasing/order-preserving partial transformations Semigroup Stirling's formula |