Hamiltonian Intervals in the Lattice of Binary Paths
I. Tasoulas,
K. Manes,
A. Sapounakis
Abstract:Let $\mathcal{P}_n$ be the set of all binary paths (i.e., lattice paths with upsteps $u = (1,1)$ and downsteps $d = (1,-1)$) of length $n$ endowed with the pointwise partial ordering (i.e., $P \le Q$ iff the lattice path $P$ lies weakly below $Q$) and let $G_n$ be its Hasse graph. For each path $P \in \mathcal{P}_n$, we denote by $I(P)$ the interval which contains the elements of $\mathcal{P}_n$ less than or equal to $P$, excluding the first two elements of $\mathcal{P}_n$, and by $G(P)$ the subgraph of $G_n$ … Show more
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