Some order-theoretic properties of the Motzkin and Schröder families∗

A Bijection Between 3-Motzkin Paths and Schröder Paths With No Peak at Odd Height

A new bijection between 3-Motzkin paths and Schröder paths with no peak at odd height is presented, together with numerous consequences involving related combinatorial structures such as 2-Motzkin paths, ordinary Motzkin paths and Dyck paths.

Inverses of Motzkin and Schröder Paths

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 Schröder matrix we look at the paths inside the same band, but ending on the top side of the band.

From (2, 3)-Motzkin Paths to Schröder Paths

In this paper, we provide a bijection between the set of restricted (2, 3)-Motzkin paths of length n and the set of Schröder paths of semilength n. Furthermore, we give a one-to-one correspondence between the set of (2, 3)-Motzkin paths of length n and the set of little Schröder paths of semilength n + 1. By applying the bijections, we get the enumerations of Schröder paths according to the sta...

THE ORDER GRAPHS OF GROUPS

Let $G$ be a group. The order graph of $G$ is the (undirected)graph $Gamma(G)$,those whose vertices are non-trivial subgroups of $G$ and two distinctvertices $H$ and $K$ are adjacent if and only if either$o(H)|o(K)$ or $o(K)|o(H)$. In this paper, we investigate theinterplay between the group-theoretic properties of $G$ and thegraph-theoretic properties of $Gamma(G)$. For a finite group$G$, we s...

Order properties of the Motzkin and Schroder families