Partial transformation monoids preserving a uniform partition
  The objective of this paper is to study the monoid of all partial transformations of a finite set that preserve a uniform partition. In addition to proving that this monoid is a quotient of a wreath product with respect to a congruence relation, we show that it is generated by 5 generators, we compute its order and determine a presentation on a minimal generating set. 
Serena Cicalo, Vitor H. Fernandes and Csaba Schneider
math.GR