TY  - JOUR
A1  - Fernandes, Vitor H.
A1  - Koppitz, Jörg
A1  - Musunthia, Tiwadee
T1  - The Rank of the Semigroup of All Order-Preserving Transformations on a Finite Fence
T2  - Bulletin of the Malaysian Mathematical Sciences Society volume
N2  - A zig-zag (or fence) order is a special partial order on a (finite) set. In this paper, we consider the semigroup TFn of all order-preserving transformations on an n-element zig-zag-ordered set. We determine the rank of TFn and provide a minimal generating set for TFn. Moreover, a formula for the number of idempotents in TFn is given.
KW  - Transformation semigroups
KW  - Rank of semigroup
KW  - Idempotents
KW  - Order-preserving
KW  - Fence
KW  - Zig-zag order
Y1  - 2019
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/48334
SN  - 0126-6705
SN  - 2180-4206
VL  - 42
IS  - 5
SP  - 2191
EP  - 2211
PB  - Malaysian mathematical sciences sciences soc
CY  - Pulau Punang
ER  -