Identifier
- St000666: Permutations ⟶ ℤ
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 0
[2,1,3] => 0
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 0
[1,3,2,4] => 0
[1,3,4,2] => 0
[1,4,2,3] => 0
[1,4,3,2] => 0
[2,1,3,4] => 0
[2,1,4,3] => 0
[2,3,1,4] => 0
[2,3,4,1] => 0
[2,4,1,3] => 0
[2,4,3,1] => 0
[3,1,2,4] => 0
[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] => 0
[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] => 0
[1,2,3,5,4] => 0
[1,2,4,3,5] => 0
[1,2,4,5,3] => 1
[1,2,5,3,4] => 0
[1,2,5,4,3] => 0
[1,3,2,4,5] => 0
[1,3,2,5,4] => 0
[1,3,4,2,5] => 0
[1,3,4,5,2] => 0
[1,3,5,2,4] => 0
[1,3,5,4,2] => 0
[1,4,2,3,5] => 0
[1,4,2,5,3] => 0
[1,4,3,2,5] => 0
[1,4,3,5,2] => 0
[1,4,5,2,3] => 0
[1,4,5,3,2] => 0
[1,5,2,3,4] => 0
[1,5,2,4,3] => 0
[1,5,3,2,4] => 0
[1,5,3,4,2] => 0
[1,5,4,2,3] => 0
[1,5,4,3,2] => 0
[2,1,3,4,5] => 0
[2,1,3,5,4] => 0
[2,1,4,3,5] => 0
[2,1,4,5,3] => 0
[2,1,5,3,4] => 0
[2,1,5,4,3] => 0
[2,3,1,4,5] => 0
[2,3,1,5,4] => 0
[2,3,4,1,5] => 0
[2,3,4,5,1] => 0
[2,3,5,1,4] => 0
[2,3,5,4,1] => 0
[2,4,1,3,5] => 0
[2,4,1,5,3] => 0
[2,4,3,1,5] => 0
[2,4,3,5,1] => 0
[2,4,5,1,3] => 0
[2,4,5,3,1] => 0
[2,5,1,3,4] => 0
[2,5,1,4,3] => 0
[2,5,3,1,4] => 0
[2,5,3,4,1] => 0
[2,5,4,1,3] => 0
[2,5,4,3,1] => 0
[3,1,2,4,5] => 1
[3,1,2,5,4] => 0
[3,1,4,2,5] => 0
[3,1,4,5,2] => 0
[3,1,5,2,4] => 0
[3,1,5,4,2] => 0
[3,2,1,4,5] => 0
[3,2,1,5,4] => 0
[3,2,4,1,5] => 0
[3,2,4,5,1] => 0
[3,2,5,1,4] => 0
[3,2,5,4,1] => 0
[3,4,1,2,5] => 0
[3,4,1,5,2] => 0
[3,4,2,1,5] => 0
[3,4,2,5,1] => 0
[3,4,5,1,2] => 0
[3,4,5,2,1] => 0
[3,5,1,2,4] => 0
[3,5,1,4,2] => 0
>>> Load all 1201 entries. <<<
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Description
The number of right tethers of a permutation.
Let $\pi$ be a permutation of length $n$. A raft of $\pi$ is a non-empty maximal sequence of consecutive small ascents, St000441The number of successions of a permutation., and a right tether is a large ascent between two consecutive rafts of $\pi$.
See Definition 3.10 and Example 3.11 in [1].
Let $\pi$ be a permutation of length $n$. A raft of $\pi$ is a non-empty maximal sequence of consecutive small ascents, St000441The number of successions of a permutation., and a right tether is a large ascent between two consecutive rafts of $\pi$.
See Definition 3.10 and Example 3.11 in [1].
References
[1] Billey, S. C., Konvalinka, M., Petersen, T. K., Slofstra, W., Tenner, B. E. Parabolic double cosets in Coxeter groups arXiv:1612.00736
Code
def statistic(pi):
rafts = [[]]
for i in range(len(pi)-1):
if pi[i+1] == pi[i]+1:
rafts[-1].append(i)
else:
rafts.append([])
rafts = [ raft for raft in rafts if raft ]
return sum(1 for i in range(len(rafts)-1)
if rafts[i][-1] + 2 == rafts[i+1][0] and pi[rafts[i][-1]+1] < pi[rafts[i+1][0]])
Created
Dec 05, 2016 at 12:20 by Christian Stump
Updated
Nov 03, 2017 at 00:22 by Martin Rubey
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