of the "dual corners" to its Young diagram (boxes outside the diagram that are the first such box both in their row and in their column). There is always a dual corner in the first row, and for each other dual corner there is a corner in the previous row, whence the stated property. If distinct partitions p and q both cover k elements of Y then k is 0 or 1, and p and q are covered by k elements. In plain language: two partitions can have at most one (third) partition covered by both (their respective diagrams then each have one box not belonging to the other), in which case there is also one (fourth) partition covering them both (whose diagram is the union of their diagrams). Saturated chains between ∅ and p are in a natural bijection with the standard Young tableaux of shape p: the diagrams in the chain add the boxes of the diagram of the standard Young tableau in the order of their numbering. More generally, saturated chains between q and p are in a natural bijection with the skew standard tableaux of skew shape p/q. The Möbius function of Young's lattice takes values 0, ±1. It is given by the formula Dihedral symmetry Conventionally, Young's lattice is depicted in a Hasse diagram with all elements of the same rank shown at the same height above the bottom. has shown that a different way of depicting some subsets of Young's lattice shows some unexpected symmetries. The partition of the nth triangular number has a Ferrers diagram that looks like a staircase. The largest elements whose Ferrers diagrams are rectangular that lie under the staircase are these: Partitions of this form are the only ones that have only one element immediately below them in Young's lattice. Suter showed that the set of all elements less than or equal to these particular partitions has not only the bilateral symmetry that one expects of Young's lattice, but also rotational symmetry: the rotation group of order n + 1 acts on this poset. Since this set has both bilateral symmetry and rotational symmetry, it must have dihedral symmetry: the (n + 1)st dihedral group acts faithfully on this set. The size of this set is 2n. For example, when n = 4, then the maximal element under the "staircase" that have rectangular Ferrers diagrams are 1 + 1