Identifier
- St001082: Permutations ⟶ ℤ
Values
[1,2] => 0
[2,1] => 0
[1,2,3] => 1
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 2
[1,2,4,3] => 2
[1,3,2,4] => 0
[1,3,4,2] => 1
[1,4,2,3] => 1
[1,4,3,2] => 0
[2,1,3,4] => 2
[2,1,4,3] => 0
[2,3,1,4] => 1
[2,3,4,1] => 1
[2,4,1,3] => 0
[2,4,3,1] => 0
[3,1,2,4] => 1
[3,1,4,2] => 0
[3,2,1,4] => 0
[3,2,4,1] => 0
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 1
[4,1,3,2] => 0
[4,2,1,3] => 0
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 3
[1,2,3,5,4] => 3
[1,2,4,3,5] => 2
[1,2,4,5,3] => 3
[1,2,5,3,4] => 3
[1,2,5,4,3] => 3
[1,3,2,4,5] => 2
[1,3,2,5,4] => 0
[1,3,4,2,5] => 2
[1,3,4,5,2] => 2
[1,3,5,2,4] => 1
[1,3,5,4,2] => 2
[1,4,2,3,5] => 2
[1,4,2,5,3] => 1
[1,4,3,2,5] => 0
[1,4,3,5,2] => 0
[1,4,5,2,3] => 2
[1,4,5,3,2] => 1
[1,5,2,3,4] => 2
[1,5,2,4,3] => 2
[1,5,3,2,4] => 0
[1,5,3,4,2] => 1
[1,5,4,2,3] => 1
[1,5,4,3,2] => 0
[2,1,3,4,5] => 3
[2,1,3,5,4] => 4
[2,1,4,3,5] => 0
[2,1,4,5,3] => 2
[2,1,5,3,4] => 2
[2,1,5,4,3] => 0
[2,3,1,4,5] => 3
[2,3,1,5,4] => 2
[2,3,4,1,5] => 2
[2,3,4,5,1] => 2
[2,3,5,1,4] => 2
[2,3,5,4,1] => 2
[2,4,1,3,5] => 1
[2,4,1,5,3] => 1
[2,4,3,1,5] => 0
[2,4,3,5,1] => 0
[2,4,5,1,3] => 1
[2,4,5,3,1] => 1
[2,5,1,3,4] => 2
[2,5,1,4,3] => 0
[2,5,3,1,4] => 1
[2,5,3,4,1] => 1
[2,5,4,1,3] => 0
[2,5,4,3,1] => 0
[3,1,2,4,5] => 3
[3,1,2,5,4] => 2
[3,1,4,2,5] => 1
[3,1,4,5,2] => 2
[3,1,5,2,4] => 1
[3,1,5,4,2] => 0
[3,2,1,4,5] => 3
[3,2,1,5,4] => 0
[3,2,4,1,5] => 2
[3,2,4,5,1] => 2
[3,2,5,1,4] => 0
[3,2,5,4,1] => 0
[3,4,1,2,5] => 2
[3,4,1,5,2] => 1
[3,4,2,1,5] => 1
[3,4,2,5,1] => 1
[3,4,5,1,2] => 1
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,4,2] => 0
[3,5,2,1,4] => 0
>>> Load all 1200 entries. <<<
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Description
The number of boxed occurrences of 123 in a permutation.
This is the number of occurrences of the pattern $123$ such that any entry between the three matched entries is either larger than the largest matched entry or smaller than the smallest matched entry.
This is the number of occurrences of the pattern $123$ such that any entry between the three matched entries is either larger than the largest matched entry or smaller than the smallest matched entry.
Code
def statistic(perm):
pattern = [1,2,3]
k = len(pattern)
R = [(i, j) for i in range(1,k) for j in range(1,k)]
return mesh_pattern_occurrences(perm, pattern, R=R)
def G(w):
return [ (x+1,y) for (x,y) in enumerate(w) ]
def mesh_pattern_occurrences(perm, pat, R=[]):
occs = 0
k = len(pat)
n = len(perm)
pat = G(pat)
perm = G(perm)
for H in Subsets(perm, k):
H = sorted(H)
X = dict(G(sorted(i for (i,_) in H)))
Y = dict(G(sorted(j for (_,j) in H)))
if H == [ (X[i], Y[j]) for (i,j) in pat ]:
X[0], X[k+1] = 0, n+1
Y[0], Y[k+1] = 0, n+1
shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]
for (i,j) in R
for (x,y) in perm
)
if not any(shady):
occs = occs + 1
return occs
Created
Jan 10, 2018 at 23:10 by Martin Rubey
Updated
Jan 10, 2018 at 23:10 by Martin Rubey
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!