  It is known that a graded lattice of rank n is supersolvable if and only if
it has an EL-labelling where the labels along any maximal chain are exactly the
numbers 1,2,...,n without repetition. These labellings are called S_n
EL-labellings, and having such a labelling is also equivalent to possessing a
maximal chain of left modular elements. In the case of an ungraded lattice,
there is a natural extension of S_n EL-labellings, called interpolating
labellings. We show that admitting an interpolating labelling is again
equivalent to possessing a maximal chain of left modular elements. Furthermore,
we work in the setting of a general bounded poset as all the above results
generalize to this case. We conclude by applying our results to show that the
lattice of non-straddling partitions, which is not graded in general, has a
maximal chain of left modular elements.
