  In this paper we introduce a new permutation statistic. This statistic counts
the number of bumps that occur during the execution of the Robinson-Schensted
procedure when applied to a given permutation. We provide several
interpretations of this bump statistic that include the tableaux shape and also
as an extremal problem concerning permutations and increasing subsequences.
Several aspects of this bump statistic are investigated from both structural
and enumerative viewpoints.
