My recent research is straying slightly into order theory, and I keep encountering a measurement which surely is defined in the literature, but so far I cannot find terminology anywhere.
Suppose $L$ is a lattice, i.e., a poset in which any two elements have a unique meet (greatest lower bound, denoted by $\wedge$) and a unique join (least upper bound, denoted by $\vee$). For $a,b \in L$, is there terminology in the literature corresponding to the following definition?
The _____ of $a$ and $b$ is the length of a maximal chain between $a \wedge b$ and $ a \vee b$.
I know that this may not be well-defined in all lattices, but I am mainly concerned with sublattices of Young's lattice (a.k.a. dominance lattice), in which I believe it is well-defined, since the length of a maximal chain between two Young diagrams is just the difference of the diagrams' sizes (ranks).