TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On the semigroup of all partial fence-preserving injections on a finite set
JF  - Journal of Algebra and Its Applications
N2  - For n∈N , let Xn={a1,a2,…,an} be an n-element set and let F=(Xn;<f) be a fence, also called a zigzag poset. As usual, we denote by In the symmetric inverse semigroup on Xn. We say that a transformation α∈In is fence-preserving if x<fy implies that xα<fyα, for all x,y in the domain of α. In this paper, we study the semigroup PFIn of all partial fence-preserving injections of Xn and its subsemigroup IFn={α∈PFIn:α−1∈PFIn}. Clearly, IFn is an inverse semigroup and contains all regular elements of PFIn. We characterize the Green’s relations for the semigroup IFn. Further, we prove that the semigroup IFn is generated by its elements with rank ≥n−2. Moreover, for n∈2N, we find the least generating set and calculate the rank of IFn.
KW  - Finite transformation semigroup
KW  - fence-preserving transformations
KW  - inverse semigroup
KW  - Green´s Relations
KW  - generators
KW  - rank
Y1  - 2017
U6  - https://doi.org/10.1142/S0219498817502231
SN  - 0219-4988
SN  - 1793-6829
VL  - 16
IS  - 12
PB  - World Scientific
CY  - Singapore
ER  -