  The Lalanne-Kreweras involution is an involution on the set of Dyck paths
which combinatorially exhibits the symmetry of the number of valleys and major
index statistics. We define piecewise-linear and birational extensions of the
Lalanne-Kreweras involution. Actually, we show that the Lalanne-Kreweras
involution is a special case of a more general operator, called rowvacuation,
which acts on the antichains of any graded poset. Rowvacuation, like the
closely related and more studied rowmotion operator, is a composition of
toggles. We obtain the piecewise-linear and birational lifts of the
Lalanne-Kreweras involution by using the piecewise-linear and birational
toggles of Einstein and Propp. We show that the number of valleys and major
index symmetry properties of the Lalanne-Kreweras involution extend to these
piecewise-linear and birational lifts.
