Coxeter-biCatalan combinatorics

Abstract

We consider several counting problems related to Coxeter-Catalan combinatorics and conjecture that the problems all have the same answer, which we call the $W$ -biCatalan number. We prove the conjecture in many cases.

Keywords

• alternating arc diagram
• doubled root poset
• twin nonnesting partitions
• twin sortable element
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]