## Synopsis

• Usage:
• Inputs:
• P, an instance of the type Poset,
• Outputs:
• i, , whether the maximal chains of $P$ are the same length

## Description

The poset $P$ is graded if all of its maximalChains are the same length.

Clearly, the $n$ chain and the $n$ booleanLattice are graded.

 i1 : n = 5; i2 : isGraded chain n o2 = true i3 : isGraded booleanLattice n o3 = true

However, the pentagon lattice is not graded.

 i4 : P = poset {{1,2}, {1,3}, {3,4}, {2,5}, {4, 5}}; i5 : isGraded P o5 = false