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Séminaire Lotharingien de Combinatoire, B60a (2009), 13 pp.

# Christian Stump

# On Bijections Between 231-Avoiding Permutations and Dyck Paths

**Abstract.**
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.

Received: May 12, 2008.
Accepted: May 18, 2009.
Final Version: September 8, 2009.

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