Geodesic
On Bijections Between 231-Avoiding Permutations and Dyck Paths
Séminaire lotharingien de combinatoire, Tome 60 (2009)

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We construct a bijection between 231-avoiding permutations and Dyck paths that sends the sum of the major index and the inverse major index of a 231-avoiding permutation to the major index of the corresponding Dyck path. Furthermore, we relate this bijection to others and exhibit a bistatistic on 231-avoiding permutations which is related to the q,t-Catalan numbers. 

@article{SLC_2009_60_a0,
     author = {Christian Stump},
     title = {On {Bijections} {Between} {231-Avoiding} {Permutations} and {Dyck} {Paths}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {60},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/SLC_2009_60_a0/}
}
TY  - JOUR
AU  - Christian Stump
TI  - On Bijections Between 231-Avoiding Permutations and Dyck Paths
JO  - Séminaire lotharingien de combinatoire
PY  - 2009
VL  - 60
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2009_60_a0/
ID  - SLC_2009_60_a0
ER  - 
%0 Journal Article
%A Christian Stump
%T On Bijections Between 231-Avoiding Permutations and Dyck Paths
%J Séminaire lotharingien de combinatoire
%D 2009
%V 60
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2009_60_a0/
%F SLC_2009_60_a0
Christian Stump. On Bijections Between 231-Avoiding Permutations and Dyck Paths. Séminaire lotharingien de combinatoire, Tome 60 (2009). http://geodesic.mathdoc.fr/item/SLC_2009_60_a0/