Figure 1

A coverage function, lattice path excursion, and rooted tree. A coverage function is depicted in (A) with its associated lattice path excursion (0,1,2,3,4,3,2,3,4,5,4,3,2,3,2,1,0) in (B). The lattice path excursion in (B) differs from the function (A) in that it records only the jumps of (A). It does not give any information regarding how long the function remains at each y-value. The rooted tree for the coverage function is in (C). The rooted tree is equivalent to the lattice path excursion (B). The red squares in (B) are the equivalence class representatives.