Type B plactic relations for r-domino tableaux
21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'09, Linz, Avusturya, 20 - 24 Temmuz 2009, ss.833-846, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Basıldığı Şehir: Linz
- Basıldığı Ülke: Avusturya
- Sayfa Sayıları: ss.833-846
- Anahtar Kelimeler: Domino tableaux, Insertion algorithm, Plactic relations
- Boğaziçi Üniversitesi Adresli: Evet
Özet
The recent work of Bonnafé et al. (2007) shows through two conjectures that r-domino tableaux have an important role in Kazhdan-Lusztig theory of type B with unequal parameters. In this paper we provide plactic relations on signed permutations which determine whether given two signed permutations have the same insertion r-domino tableaux in Garfinkle's algorithm (1990). Moreover, we show that a particular extension of these relations can describe Garfinkle's equivalence relation on r-domino tableaux which is given through the notion of open cycles. With these results we enunciate the conjectures of Bonnafé et al. and provide necessary tool for their proofs. © 2009 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.