Plactic relations for r-domino tableaux
Electronic Journal of Combinatorics, cilt.19, 2012 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 19
- Basım Tarihi: 2012
- Doi Numarası: 10.37236/2042
- Dergi Adı: Electronic Journal of Combinatorics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Boğaziçi Üniversitesi Adresli: Evet
Özet
The work of C. Bonnafe ́, M.Geck, L. Iancu and T. Lam [3] 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 two given signed permutations have the same insertion r-domino tableaux in Garfinkle's algorithm [4]. Moreover, we show that a particular extension of these relations can describe Garfinkle's equivalence relation [4] on r-domino tableaux which is given through the notion of open cycles. With these results we enunciate the conjectures of [3] and provide necessary tools for their proofs.