Lattice paths with infinitely many down steps -- the negative boundary model

Abstract

We consider a variation of Dyck paths, where additionally to steps $(1,1)$ and $(1,-1)$ down-steps $(1,-j)$, for $j\ge 2$ are allowed. We give credits to Emeric Deutsch for that. The enumeration of such objects living in a strip is performed. Methods are the kernel method and techniques from linear algebra.

Very early draft. Suggestions are welcome!

References in corpus (1)

• Non-decreasing Deutsch paths