Abstract
A Motzkin path is a path starting and ending on the x-axis which uses up, down and level steps and never goes below the x-axis. We consider Motzkin paths where any number of level steps on the x-axis are allowed to be marked. It is known that the number of such paths corresponds to a matrix which turns out to be a pseudo-involution in the Riordan group. We provide a combinatorial proof of this result by means of a sign-reversing involution on pairs of signed marked Motzkin paths. We also extend this result to the class of matrices that count Motzkin paths where level steps at a fixed height are allowed to be marked.
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