### Abstract

Let X_{n} = {1, 2,..., n}. On a partial transformation α: Dom α ⊆ Xn! Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is {pipe} Dom α {pipe}, the height of α is {pipe} Im α {pipe}, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OP_{n}, the semigroup of orientation-preserving full transformations of X_{n}, POP_{n} the semigroup of orientation-preserving partial transformations of X_{n}, OR_{n} the semigroup of orientation-preserving/reversing full transformations of X_{n}, and POR_{n} the semigroup of orientation-preserving/reversing partial transformations of X_{n}, and their partial one-to-one analogue semigroups, POPI_{n} and PORI_{n}.

Original language | English |
---|---|

Journal | Journal of Integer Sequences |

Volume | 14 |

Issue number | 7 |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- Anti-cyclic sequence
- Breadth
- Cyclic sequence
- Full transformation
- Height
- Left waist
- Orientation-preserving transformation
- Orientation-reversing transformation
- Partial one-to-one transformation
- Partial transformation
- Right waist

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

**Combinatorial results for semigroups of orientation-preserving partial transformations.** / Umar, A.

Research output: Contribution to journal › Article

*Journal of Integer Sequences*, vol. 14, no. 7.

}

TY - JOUR

T1 - Combinatorial results for semigroups of orientation-preserving partial transformations

AU - Umar, A.

PY - 2011

Y1 - 2011

N2 - Let Xn = {1, 2,..., n}. On a partial transformation α: Dom α ⊆ Xn! Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is {pipe} Dom α {pipe}, the height of α is {pipe} Im α {pipe}, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OPn, the semigroup of orientation-preserving full transformations of Xn, POPn the semigroup of orientation-preserving partial transformations of Xn, ORn the semigroup of orientation-preserving/reversing full transformations of Xn, and PORn the semigroup of orientation-preserving/reversing partial transformations of Xn, and their partial one-to-one analogue semigroups, POPIn and PORIn.

AB - Let Xn = {1, 2,..., n}. On a partial transformation α: Dom α ⊆ Xn! Im α ⊆ Xn of Xn the following parameters are defined: the breadth or width of α is {pipe} Dom α {pipe}, the height of α is {pipe} Im α {pipe}, and the right (resp., left) waist of α is max(Im α) (resp., min(Im α)). We compute the cardinalities of some equivalences defined by equalities of these parameters on OPn, the semigroup of orientation-preserving full transformations of Xn, POPn the semigroup of orientation-preserving partial transformations of Xn, ORn the semigroup of orientation-preserving/reversing full transformations of Xn, and PORn the semigroup of orientation-preserving/reversing partial transformations of Xn, and their partial one-to-one analogue semigroups, POPIn and PORIn.

KW - Anti-cyclic sequence

KW - Breadth

KW - Cyclic sequence

KW - Full transformation

KW - Height

KW - Left waist

KW - Orientation-preserving transformation

KW - Orientation-reversing transformation

KW - Partial one-to-one transformation

KW - Partial transformation

KW - Right waist

UR - http://www.scopus.com/inward/record.url?scp=80053068522&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053068522&partnerID=8YFLogxK

M3 - Article

VL - 14

JO - Journal of Integer Sequences

JF - Journal of Integer Sequences

SN - 1530-7638

IS - 7

ER -