On bijections between 231-avoiding permutations and Dyck paths

Details On bijections between 231-avoiding permutations and Dyck paths On bijections between 231-avoiding permutations and Dyck paths

2008-03-26

arxiv.org/abs/0803.3706v3

Mathematics

Combinatorics

13 pages, the author is very grateful to Matteo Silimbani for providing a proof of Conjecture 5.10

Scientific paper

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.

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