hasse.py

from itertools import *

# Compute our D(pi) function
elements = {}
for p in permutations([1,2,3,4]):
    d = [i+1 for i in range(3) if p[i] > p[i + 1]]
    elements[p] = frozenset(d)
    
# Make a graph with the given pi < tau relation.
graph = {}
for p1 in elements.keys():
    for p2 in elements.keys():
        d1 = elements[p1]
        d2 = elements[p2]
        graph[(p1, p2)] = d1.issubset(d2) and d1 != d2
        
print(sum(x for x in graph.values()))
        
# Remove all edges that follow from transitivity.
for p1 in elements.keys():
    for p2 in elements.keys():
        for p3 in elements.keys():
            if p1 == p2 or p2 == p3 or p3 == p1:
                continue
            if graph[(p1, p2)] and graph[(p2, p3)] and graph[(p1, p3)]:
                graph[(p1, p3)] = False
                
print(sum(x for x in graph.values()))
                
# Remove all self-edges (shouldn't be any to begin with)
for p1 in elements.keys():
    graph[(p1, p1)] = False

print(sum(x for x in graph.values()))
    
# Plot the graph
print("digraph {")
for (p1, p2), f in graph.items():
    if not f: continue
    p1 = ''.join(str(x) for x in p1)
    p2 = ''.join(str(x) for x in p2)
    print('"%s" -> "%s"' % (p1, p2))
print("}")