Counting peaks and valleys in $k$-colored Motzkin paths

A. Sapounakis, P. Tsikouras

Abstract


This paper deals with the enumeration of $k$-colored Motzkin paths with a fixed number of (left and right) peaks and valleys. Further enumeration results are obtained when peaks and valleys are counted at low and high level. Many well-known results for Dyck paths are obtained as special cases.


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