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 $f(a) < f(b)$.
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):
P = P.relabel()
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
Nov 13, 2022 at 11:37 by Martin Rubey
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