Ordering the Levels $L_k$ and $L_{k+1}$ of $\mathcal{B}_{2k+1}$
Italo Jose Dejter · arXiv (Cornell University) · 2010
A system of numeration in which every $k$, with $0<k\in\mathbb{Z}$, appears as a restricted growth string, or RGS, has the $k$-th Catalan number as the RGS $10^k$. This induces a canonical ordering of the vertices of the dihedral quotients of the middle-levels graphs.