Generalized triangulations, pipe dreams, and simplicial spheres
Abstrak
We exhibit a canonical connection between maximal $(0,1)$-fillings of a moon polyomino avoiding north-east chains of a given length and reduced pipe dreams of a certain permutation. Following this approach we show that the simplicial complex of such maximal fillings is a vertex-decomposable and thus a shellable sphere. In particular, this implies a positivity result for Schubert polynomials. For Ferrers shapes, we moreover construct a bijection to maximal fillings avoiding south-east chains of the same length which specializes to a bijection between $k$-triangulations of the $n$-gon and $k$-fans of Dyck paths. Using this, we translate a conjectured cyclic sieving phenomenon for $k$-triangulations with rotation to $k$-flagged tableaux with promotion.
Topik & Kata Kunci
Penulis (2)
Luis Serrano
Christian Stump
Akses Cepat
- Tahun Terbit
- 2011
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2961
- Akses
- Open Access ✓