9 citations · 15 across the 4 of their papers we have counts for
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Inverses of Motzkin and Schröder Paths
Heinrich Niederhausen
We suggest three applications for the inverses: For the inverse Motzkin matrix we look at Hankel determinants, and counting the paths inside a horizontal band, and for the inverse…
The classical umbral calculus: Sheffer sequences
E. Di Nardo, H. Niederhausen, D. Senato
Following the approach of Rota and Taylor \cite{SIAM}, we present an innovative theory of Sheffer sequences in which the main properties are encoded by using umbrae. This syntax al…
Pattern Avoiding Ballot Paths and Finite Operator Calculus
Heinrich Niederhausen, Shaun Sullivan
Counting pattern avoiding ballot paths begins with a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in…
Euler Coefficients and Restricted Dyck Paths
Heinrich Niederhausen, Shaun Sullivan
We consider the problem of enumerating Dyck paths staying weakly above the x-axis with a limit to the number of consecutive up steps, or a limit to the number of consecutive down s…