IJPAM: Volume 86, No. 3 (2013)

COMBINATORIAL RESULTS FOR SEMIGROUPS OF
ORDER-PRESERVING FULL TRANSFORMATIONS
WITH PATTERN OF RANGE

Phichet Jitjankarn
Division of Mathematics
School of Science
Walailak University
Nakhon Si Thammarat, 80161, THAILAND


Abstract. Let O[n] and C[n] be the semigroup of all order-preserving and all order-preserving and regressive transformations on the set [n]={1,...,n}, respectively. In this paper, we give a pattern on [n]. Combinatorial properties on subsemigroups of O[n] with restricted range to the pattern are investigated.

Received: March 1, 2013

AMS Subject Classification: 20M20, 11B39

Key Words and Phrases: order-preserving transformation semigroups, regressive transformation semigroups, Fibonacci numbers, Catalan numbers

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DOI: 10.12732/ijpam.v86i3.4 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 86
Issue: 3