Balanced labellings of affine permutations
Abstrak
We study the $\textit{diagrams}$ of affine permutations and their $\textit{balanced}$ labellings. As in the finite case, which was investigated by Fomin, Greene, Reiner, and Shimozono, the balanced labellings give a natural encoding of reduced decompositions of affine permutations. In fact, we show that the sum of weight monomials of the $\textit{column strict}$ balanced labellings is the affine Stanley symmetric function defined by Lam and we give a simple algorithm to recover reduced words from balanced labellings. Applying this theory, we give a necessary and sufficient condition for a diagram to be an affine permutation diagram. Finally, we conjecture that if two affine permutations are $\textit{diagram equivalent}$ then their affine Stanley symmetric functions coincide.
Topik & Kata Kunci
Penulis (2)
Hwanchul Yoo
Taedong Yun
Akses Cepat
- Tahun Terbit
- 2013
- Sumber Database
- DOAJ
- DOI
- 10.46298/dmtcs.2342
- Akses
- Open Access ✓