We study some statistics related to Dyck paths, whose explicit formulas are obtained by means of the Lagrange Inversion Theorem. There are five such statistics and one of them is well-known and owed to Narayana. The most interesting of the other four statistics is related to Euler's trinomial coefficients and to Motzkin numbers: we perform a study of that statistic proving a number of its properties.
Some statistics on Dyck paths / D. MERLINI; R. SPRUGNOLI; M. VERRI. - In: JOURNAL OF STATISTICAL PLANNING AND INFERENCE. - ISSN 0378-3758. - STAMPA. - 101:(2002), pp. 211-227. [10.1016/S0378-3758(01)00180-X]
Some statistics on Dyck paths
MERLINI, DONATELLA;SPRUGNOLI, RENZO;VERRI, MARIA CECILIA
2002
Abstract
We study some statistics related to Dyck paths, whose explicit formulas are obtained by means of the Lagrange Inversion Theorem. There are five such statistics and one of them is well-known and owed to Narayana. The most interesting of the other four statistics is related to Euler's trinomial coefficients and to Motzkin numbers: we perform a study of that statistic proving a number of its properties.
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