Collapsing monoids consisting of permutations and constants

In this paper we determine all collapsing transformation monoids that contain at least one unary constant operation and whose nonconstant operations are permutations. Furthermore, we find an infinite family of transformation monoids that consist of at least three unary constant operations and some permutations for which the corresponding monoidal intervals are 2-element chains. This research is supported by Hungarian National Foundation for Scientific Research grant nos. T 37877 and K 60148.