Journal of Integer Sequences, Vol. 14 (2011), Article 11.7.5 |

Department of Mathematics and Statistics

Sultan Qaboos University

Al-Khod, PC 123

Sultanate of Oman

**Abstract:**

Let
. On a partial transformation
Im of the following parameters are defined: the
*breadth or width* of is
,
the *height* of is
Im , and the
*right (resp., left) waist* of is
Im
(resp.,
Im ). We compute the cardinalities of some
equivalences defined by equalities of these parameters on
, the semigroup of orientation-preserving full transformations
of ,
the semigroup of orientation-preserving
partial transformations of ,
the semigroup of
orientation-preserving/reversing full transformations of , and
the semigroup of orientation-preserving/reversing
partial transformations of , and their partial one-to-one
analogue semigroups,
and
.

(Concerned with sequences A000225 A000290 A002061 A066524 A163102.)

Received September 19 2010;
revised version received July 9 2011.
Published in *Journal of Integer Sequences*, September 5 2011.

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