On the interaction of the Coxeter transformation and the rowmotion bijection
Journal of Combinatorial Algebra, cilt.8, sa.3, ss.359-374, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 8 Sayı: 3
- Basım Tarihi: 2024
- Doi Numarası: 10.4171/jca/101
- Dergi Adı: Journal of Combinatorial Algebra
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.359-374
- Anahtar Kelimeler: Coxeter transformation, distributive lattices, grade bijection
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Galatasaray Üniversitesi Adresli: Evet
Özet
Let P be a finite poset and L the associated distributive lattice of order ideals of P . Let Ρ denote the rowmotion bijection of the order ideals of P viewed as a permutation matrix and C the Coxeter matrix for the incidence algebra kL of L. Then, we show the identity .Ρ-1C /2 D id, as was originally conjectured by Sam Hopkins. Recently, it was noted that the rowmotion bijection is a special case of the much more general grade bijection R that exists for any Auslander regular algebra. This motivates to study the interaction of the grade bijection and the Coxeter matrix for general Auslander regular algebras. For the class of higher Auslander algebras coming from n-representation finite algebras, we show that .R-1C /2 D id if n is even and .R-1C C id/2 D 0 when n is odd.