Dyck path enumeration
Dyck paths of semilength \(n\) are paths from (0, 0) to \((2n,0)\) with steps (1, 1) and \((1,-1)\) which lie on or above the \(x\)-axis. The paper gives a systematic treatment to the enumeration of Dyck paths according to semilength and one more statistics. Many known and some new facts are proved, mostly using generating functions and Lagrange inversion. The elementary technique presented, which is an alternative of the closely related Schützenberger methodology, can also be applied to Motzkin paths, Schröder paths, noncrossing partitions, ordered trees, to certain classes of polyominoes, and probably to many other problems.
scientific article; zbMATH DE number 1331472
scientific article