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Abstract: Two combinatorial statistics, the pyramid weight and the number of exterior pairs, are investigated on the set of Dyck paths. Explicit formulae are given for the generating functions of Dyck paths of prescribed pyramid weight and prescribed number of exterior pairs. The proofs are combinatorial and rely on the method of q-grammars as well as on two new q-analogues of the Catalan numbers derived from statistics on noncrossing partitions. Connections with the combinatorics of Motzkin paths ... (Update)
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...correspondence. Recent work involving inversions, major indices, and permutation statistics is presented in [7, 9, 12, 30, 31, 32, 33, 34, 35, 36, 39, 40]. Proportionally speaking, w i statistics are rather scarce. For example, there are over 1662 trillion Mahonian...
...cardinality of D n is mn 1 Gamma mn n . For the classic m = 1 case, this becomes the nth Catalan number, Cn = Denise and Simion [5] cite several other combinatorial objects which are enumerated by the Catalan numbers and give two new statistics on ordinary (m = 1) Dyck...
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BibTeX entry: (Update)
A. Denise and R. Simion, Two combinatorial statistics on Dyck paths, Discrete Math. 137 (1995), 155--176. http://citeseer.ist.psu.edu/denise92two.html More
@misc{ denise95two,
author = "A. Denise and R. Simion",
title = "Two combinatorial statistics on Dyck paths",
text = "A. Denise and R. Simion, Two combinatorial statistics on Dyck paths, Discrete
Math. 137 (1995), 155--176.",
year = "1995",
url = "citeseer.ist.psu.edu/denise92two.html" }
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