Reduced Words for Clans
Abstract
Clans are combinatorial objects indexing the orbits of $\text{GL}(\mathbb{C}^p) \times \text{GL}(\mathbb{C}^q)$ on the variety of flags in $\mathbb{C}^{p+q}$. This geometry leads to a partial order on the set of clans analogous to weak Bruhat order on the symmetric group, and we study the saturated chains in this order. We prove an analogue of Tits' theorem on reduced words in a Coxeter group. We also obtain enumerations of reduced word sets for particular clans in terms of standard tableaux and shifted standard tableaux.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Advanced Algebra and Geometry
Algebraic structures and combinatorial models
Publication details
- Journal / source
- The Electronic Journal of Combinatorics
- Publisher
- The Electronic Journal of Combinatorics
- Volume
- 33
- Issue
- 2
- Publication date
- 18 June 2026
- Language
- EN