Identifier
Identifier
Values
=>
Cc0014;cc-rep
([],2)=>4 ([(0,1)],2)=>1 ([],3)=>27 ([(1,2)],3)=>3 ([(0,1),(0,2)],3)=>4 ([(0,2),(2,1)],3)=>1 ([(0,2),(1,2)],3)=>4 ([],4)=>256 ([(2,3)],4)=>16 ([(1,2),(1,3)],4)=>16 ([(0,1),(0,2),(0,3)],4)=>27 ([(0,2),(0,3),(3,1)],4)=>2 ([(0,1),(0,2),(1,3),(2,3)],4)=>4 ([(1,2),(2,3)],4)=>4 ([(0,3),(3,1),(3,2)],4)=>4 ([(1,3),(2,3)],4)=>16 ([(0,3),(1,3),(3,2)],4)=>4 ([(0,3),(1,3),(2,3)],4)=>27 ([(0,3),(1,2)],4)=>4 ([(0,3),(1,2),(1,3)],4)=>8 ([(0,2),(0,3),(1,2),(1,3)],4)=>16 ([(0,3),(2,1),(3,2)],4)=>1 ([(0,3),(1,2),(2,3)],4)=>2 ([],5)=>3125 ([(3,4)],5)=>125 ([(2,3),(2,4)],5)=>100 ([(1,2),(1,3),(1,4)],5)=>135 ([(0,1),(0,2),(0,3),(0,4)],5)=>256 ([(0,2),(0,3),(0,4),(4,1)],5)=>9 ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>12 ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>27 ([(1,3),(1,4),(4,2)],5)=>10 ([(0,3),(0,4),(4,1),(4,2)],5)=>8 ([(1,2),(1,3),(2,4),(3,4)],5)=>20 ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>4 ([(0,3),(0,4),(3,2),(4,1)],5)=>4 ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>8 ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>16 ([(2,3),(3,4)],5)=>25 ([(1,4),(4,2),(4,3)],5)=>20 ([(0,4),(4,1),(4,2),(4,3)],5)=>27 ([(2,4),(3,4)],5)=>100 ([(1,4),(2,4),(4,3)],5)=>20 ([(0,4),(1,4),(4,2),(4,3)],5)=>16 ([(1,4),(2,4),(3,4)],5)=>135 ([(0,4),(1,4),(2,4),(4,3)],5)=>27 ([(0,4),(1,4),(2,4),(3,4)],5)=>256 ([(0,4),(1,4),(2,3)],5)=>15 ([(0,4),(1,3),(2,3),(2,4)],5)=>24 ([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>55 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>108 ([(0,4),(1,4),(2,3),(4,2)],5)=>4 ([(0,4),(1,3),(2,3),(3,4)],5)=>8 ([(0,4),(1,4),(2,3),(2,4)],5)=>38 ([(0,4),(1,4),(2,3),(3,4)],5)=>9 ([(1,4),(2,3)],5)=>20 ([(1,4),(2,3),(2,4)],5)=>40 ([(0,4),(1,2),(1,4),(2,3)],5)=>3 ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>8 ([(1,3),(1,4),(2,3),(2,4)],5)=>80 ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>8 ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>16 ([(0,4),(1,2),(1,4),(4,3)],5)=>6 ([(0,4),(1,2),(1,3)],5)=>15 ([(0,4),(1,2),(1,3),(1,4)],5)=>38 ([(0,2),(0,4),(3,1),(4,3)],5)=>2 ([(0,4),(1,2),(1,3),(3,4)],5)=>4 ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>1 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>12 ([(0,3),(0,4),(1,2),(1,4)],5)=>24 ([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>55 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>108 ([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>1 ([(0,3),(1,2),(1,4),(3,4)],5)=>3 ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>8 ([(1,4),(3,2),(4,3)],5)=>5 ([(0,3),(3,4),(4,1),(4,2)],5)=>4 ([(1,4),(2,3),(3,4)],5)=>10 ([(0,4),(1,2),(2,4),(4,3)],5)=>2 ([(0,3),(1,4),(4,2)],5)=>3 ([(0,4),(3,2),(4,1),(4,3)],5)=>2 ([(0,4),(1,2),(2,3),(2,4)],5)=>6 ([(0,4),(2,3),(3,1),(4,2)],5)=>1 ([(0,3),(1,2),(2,4),(3,4)],5)=>4 ([(0,4),(1,2),(2,3),(3,4)],5)=>2 ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>4
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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