We study some statistics related to Dyck paths, whose explicit formulas are obtained by means of the Lagrange Inversion Formula. There are five such statistics and one of them is well-known and owed to Narayana. The most interesting of the other 4 statistics is related to Euler's trinomial coefficients: we perform a study of that statistic proving a number of its properties.
Lagrange statistics on Dyck paths / D. Merlini; R. Sprugnoli; M. C. Verri. - STAMPA. - (1998), pp. 1-14. (Intervento presentato al convegno Lattice Paths Combinatorics and Applications '98 tenutosi a Wien, Austria nel July 8-10, 1998).
Lagrange statistics on Dyck paths
MERLINI, DONATELLA;SPRUGNOLI, RENZO;VERRI, MARIA CECILIA
1998
Abstract
We study some statistics related to Dyck paths, whose explicit formulas are obtained by means of the Lagrange Inversion Formula. There are five such statistics and one of them is well-known and owed to Narayana. The most interesting of the other 4 statistics is related to Euler's trinomial coefficients: we perform a study of that statistic proving a number of its properties.
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