Abstract
Let script P sign script C sign n be the semigroup of all decreasing and order-preserving partial transformations of an n -element chain, and let E (script P sign script C sign n ) be its set of idempotents. Among other results, asymptotic formulae for |script P sign script C sign n | and | E (script P sign script C sign n )|/|script P sign script C sign n | are obtained. Similar results for script P sign script O sign n the (larger) semigroup of all order-preserving partial transformations of an n -element chain are also obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 1071-1075 |
| Number of pages | 5 |
| Journal | Communications in Algebra |
| Volume | 34 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Feb 2006 |
| Externally published | Yes |
Keywords
- Double/small Schröder number
- Generating function
- Idempotents
- Integral representation
- Legendre polynomial
- Order-decreasing/order-preserving partial transformations
- Semigroup
- Stirling's formula
ASJC Scopus subject areas
- Algebra and Number Theory