Hasse Diagram Level Calculator

About this calculator

A Hasse diagram is a simplified visualization of a partial order that omits reflexive and transitive edges, drawing only the direct "covers" relations, with elements arranged so that a higher position means "greater" under the order. For the divisibility partial order on a set of positive integers, one element covers another when it's a direct multiple with no divisor of the set in between, and the level (rank) of an element reflects how many such covering steps separate it from the diagram's minimal elements.

This calculator takes a set of positive integers, builds the divisibility relation among them, and assigns each element its level in the resulting Hasse diagram. Discrete mathematics and order theory students use it to check homework on lattices and partial orders, since manually tracing covering relations and levels for more than a handful of numbers is tedious and error-prone by hand.