OFFSET
0,8
COMMENTS
DE(n,k) = number of permutations with d descents and e descents of the inverse such that d+e = k.
REFERENCES
Christian Stump, On bijections between 231-avoiding permutations and Dyck paths, MathSciNet:2734176
LINKS
Dominique Foata and Guo-Niu Han, The q-series in Combinatorics; permutation statistics
FindStat - Combinatorial Statistic Finder, The sum of the number of descents and the number of recoils of a permutation
EXAMPLE
The triangle DE(n, k) begins:
n\k 0 1 2 3 4 5 6 7 8 9 10
0: 1
1: 1
2: 1 0 1
3: 1 0 4 0 1
4: 1 0 10 2 10 0 1
5: 1 0 20 12 54 12 20 0 1
6: 1 0 35 42 212 140 212 42 35 0 1
PROG
(SageMath)
q = var("q")
[sum( q^(pi.number_of_descents()+pi.inverse().number_of_descents()) for pi in Permutations(n) ).coefficients(sparse=False) for n in [1 .. 6]]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Christian Stump, Jan 16 2018
STATUS
approved