Journal of Integer Sequences, Vol. 7 (2004), Article 04.3.8

Combinatorial Results for Semigroups of Order-Decreasing Partial Transformations

A. Laradji and A. Umar
Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals
Dhahran 31261
Saudi Arabia

Abstract: Let PCn be the semigroup of all decreasing and order-preserving partial transformations of a finite chain. It is shown that |PCn| = rn, where rn is the large (or double) Schröder number. Moreover, the total number of idempotents of PCn is shown to be (3n+1)/2.

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(Concerned with sequences A001263 A082137 .)

Received October 25 2003; revised version received July 31 2004. Published in Journal of Integer Sequences October 17 2004.

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