Involutions on Baxter Objects

Abstract

Baxter numbers are known to count several families of combinatorial objects, all of which come equipped with natural involutions. In this paper, we add a combinatorial family to the list, and show that the known bijections between these objects respect these involutions. We also give a formula for the number of objects fixed under this involution, showing that it is an instance of Stembridge's "$q=-1$ phenomenon''.

Keywords

• bijections
• baxter permutations
• involutions
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]