maximal chain

A maximal chain is a sequence of elements arranged in a specific order where each element is directly related to the next, and you cannot add any more elements to extend this sequence without breaking its order. Think of it like climbing a ladder: each rung represents an element, and a maximal chain goes as far up as possible without skipping steps or being able to add another rung without changing the existing links. In mathematical terms, it's the longest possible chain within a set that respects a certain ordering, capturing the most extensive hierarchical or layered structure present.