Matchings Avoiding Partial Patterns and Lattice Paths

In this paper, we consider matchings avoiding partial patterns 1123 and 1132. We give a bijection between 1123-avoiding matchings with n edges and nonnegative lattice paths from (0, 2) to (2n, 0). As a consequence, the refined enumeration of 1123-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a bijection between 1132-avoiding matchings with n edges and lattice paths from (0, 0) to (2n, 0) starting with an up step, which may go under the x-axis.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: Vít Jelínek, Nelson Y. Li, Toufik Mansour, Sherry H. F. Yan
• Keywords: COMBINATORICS 2006, Lattice Paths, Nonnegative Lattice Paths, Partial Patterns