  It is well known that Thom-Boardman symbols are realized by non-increasing
sequences of nonnegative integers. A natural question is whether the converse
is also true. In this paper we answer this question affirmatively, that is, for
any non-increasing sequence of nonnegative integers, there is a map-germ with
the prescribed sequence as its Thom-Boardman symbol.

Commutative Algebra;Algebraic Geometry