## Michael W. Schroeder ; Rebecca Smith - A Bijection on Classes Enumerated by the Schröder Numbers

dmtcs:1326 - Discrete Mathematics & Theoretical Computer Science, July 19, 2017, Vol. 18 no. 2, Permutation Patterns 2015 - https://doi.org/10.46298/dmtcs.1326
A Bijection on Classes Enumerated by the Schröder Numbers

Authors: Michael W. Schroeder ; Rebecca Smith

We consider a sorting machine consisting of two stacks in series where the first stack has the added restriction that entries in the stack must be in decreasing order from top to bottom. The class of permutations sortable by this machine are known to be enumerated by the Schröder numbers. In this paper, we give a bijection between these sortable permutations of length $n$ and Schröder paths -- the lattice paths from $(0,0)$ to $(n-1,n-1)$ composed of East steps $(1,0)$, North steps $(0,1)$, and Diagonal steps $(1,1)$ that travel weakly below the line $y=x$.

Volume: Vol. 18 no. 2, Permutation Patterns 2015
Section: Permutation Patterns
Published on: July 19, 2017
Accepted on: July 19, 2017
Submitted on: July 16, 2017
Keywords: Mathematics - Combinatorics,05A05