Subwords and Plane Partitions

Abstract

Using the powerful machinery available for reduced words of type $B$, we demonstrate a bijection between centrally symmetric $k$-triangulations of a $2(n + k)$-gon and plane partitions of height at most $k$ in a square of size $n$. This bijection can be viewed as the type $B$ analogue of a bijection for $k$-triangulations due to L. Serrano and C. Stump.

Keywords

• little bump
• insertion
• reduced word
• linear extension
• centrally symmetric $k$-triangulation
• subword complex
• plane partition
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]