Identifier
Identifier
Values
([],2) generating graphics... => 4
([(0,1)],2) generating graphics... => 1
([],3) generating graphics... => 27
([(1,2)],3) generating graphics... => 3
([(0,1),(0,2)],3) generating graphics... => 4
([(0,2),(2,1)],3) generating graphics... => 1
([(0,2),(1,2)],3) generating graphics... => 4
([],4) generating graphics... => 256
([(2,3)],4) generating graphics... => 16
([(1,2),(1,3)],4) generating graphics... => 16
([(0,1),(0,2),(0,3)],4) generating graphics... => 27
([(0,2),(0,3),(3,1)],4) generating graphics... => 2
([(0,1),(0,2),(1,3),(2,3)],4) generating graphics... => 4
([(1,2),(2,3)],4) generating graphics... => 4
([(0,3),(3,1),(3,2)],4) generating graphics... => 4
([(1,3),(2,3)],4) generating graphics... => 16
([(0,3),(1,3),(3,2)],4) generating graphics... => 4
([(0,3),(1,3),(2,3)],4) generating graphics... => 27
([(0,3),(1,2)],4) generating graphics... => 4
([(0,3),(1,2),(1,3)],4) generating graphics... => 8
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 16
([(0,3),(2,1),(3,2)],4) generating graphics... => 1
([(0,3),(1,2),(2,3)],4) generating graphics... => 2
([],5) generating graphics... => 3125
([(3,4)],5) generating graphics... => 125
([(2,3),(2,4)],5) generating graphics... => 100
([(1,2),(1,3),(1,4)],5) generating graphics... => 135
([(0,1),(0,2),(0,3),(0,4)],5) generating graphics... => 256
([(0,2),(0,3),(0,4),(4,1)],5) generating graphics... => 9
([(0,1),(0,2),(0,3),(2,4),(3,4)],5) generating graphics... => 12
([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) generating graphics... => 27
([(1,3),(1,4),(4,2)],5) generating graphics... => 10
([(0,3),(0,4),(4,1),(4,2)],5) generating graphics... => 8
([(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 20
([(0,2),(0,3),(2,4),(3,4),(4,1)],5) generating graphics... => 4
([(0,3),(0,4),(3,2),(4,1)],5) generating graphics... => 4
([(0,2),(0,3),(2,4),(3,1),(3,4)],5) generating graphics... => 8
([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 16
([(2,3),(3,4)],5) generating graphics... => 25
([(1,4),(4,2),(4,3)],5) generating graphics... => 20
([(0,4),(4,1),(4,2),(4,3)],5) generating graphics... => 27
([(2,4),(3,4)],5) generating graphics... => 100
([(1,4),(2,4),(4,3)],5) generating graphics... => 20
([(0,4),(1,4),(4,2),(4,3)],5) generating graphics... => 16
([(1,4),(2,4),(3,4)],5) generating graphics... => 135
([(0,4),(1,4),(2,4),(4,3)],5) generating graphics... => 27
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 256
([(0,4),(1,4),(2,3)],5) generating graphics... => 15
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 24
([(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 55
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 108
([(0,4),(1,4),(2,3),(4,2)],5) generating graphics... => 4
([(0,4),(1,3),(2,3),(3,4)],5) generating graphics... => 8
([(0,4),(1,4),(2,3),(2,4)],5) generating graphics... => 38
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 9
([(1,4),(2,3)],5) generating graphics... => 20
([(1,4),(2,3),(2,4)],5) generating graphics... => 40
([(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 3
([(0,3),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 8
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 80
([(0,3),(0,4),(1,3),(1,4),(4,2)],5) generating graphics... => 8
([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) generating graphics... => 16
([(0,4),(1,2),(1,4),(4,3)],5) generating graphics... => 6
([(0,4),(1,2),(1,3)],5) generating graphics... => 15
([(0,4),(1,2),(1,3),(1,4)],5) generating graphics... => 38
([(0,2),(0,4),(3,1),(4,3)],5) generating graphics... => 2
([(0,4),(1,2),(1,3),(3,4)],5) generating graphics... => 4
([(0,2),(0,3),(1,4),(2,4),(3,1)],5) generating graphics... => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 12
([(0,3),(0,4),(1,2),(1,4)],5) generating graphics... => 24
([(0,3),(0,4),(1,2),(1,3),(1,4)],5) generating graphics... => 55
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5) generating graphics... => 108
([(0,3),(0,4),(1,2),(1,3),(2,4)],5) generating graphics... => 1
([(0,3),(1,2),(1,4),(3,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,2),(2,3),(2,4)],5) generating graphics... => 8
([(1,4),(3,2),(4,3)],5) generating graphics... => 5
([(0,3),(3,4),(4,1),(4,2)],5) generating graphics... => 4
([(1,4),(2,3),(3,4)],5) generating graphics... => 10
([(0,4),(1,2),(2,4),(4,3)],5) generating graphics... => 2
([(0,3),(1,4),(4,2)],5) generating graphics... => 3
([(0,4),(3,2),(4,1),(4,3)],5) generating graphics... => 2
([(0,4),(1,2),(2,3),(2,4)],5) generating graphics... => 6
([(0,4),(2,3),(3,1),(4,2)],5) generating graphics... => 1
([(0,3),(1,2),(2,4),(3,4)],5) generating graphics... => 4
([(0,4),(1,2),(2,3),(3,4)],5) generating graphics... => 2
([(0,3),(1,4),(2,4),(3,1),(3,2)],5) generating graphics... => 4
click to show generating function       
Description
The number of strictly order preserving maps of a poset into itself.
A map $f$ is strictly order preserving if $a < b$ implies $f(a) < f(b)$.
References
[1] Alexandersson, P. Whether a total order set of size $n$ has the fewest endomorphisms among posets of size $n$ MathOverflow:252913
Code
def is_strictly_order_preserving(f, P):
    return all([f(a),f(b)] in P.cover_relations() for (a, b) in P.cover_relations())

def statistic(P):
    r = P.cardinality()
    S = cartesian_product([range(r)]*r)
    return len([pi for pi in S if is_strictly_order_preserving(lambda i: pi[i], P)])
 
Created
Oct 25, 2016 at 12:01 by Martin Rubey
Updated
Oct 25, 2016 at 12:14 by Martin Rubey