Les algèbres amassées

Cette page est un tableau des nombres d'amas (Clusters) pour les groupes de Coxeter finis.

Groupe W	Amas	Amas positifs	Chaines maximales	Parties exceptionnelles	Intervalles noncroisés
An	binomial(2n+2,n)/(n+1)	binomial(2n,n)/(n+1)	(n+1)n-1	binomial(3n,n)/(2n+1)	binomial(3n+3,n+1)/(2n+3)
Bn Cn	binomial(2n,n)	binomial(2n-1,n)	nn	binomial(3n-2,n-1)	binomial(3n,n)
Dn	(3n-2) binomial(2n-2,n-1)/n	(3n-4) binomial(2n-3,n-1)/n	2(n-1)n	(16n2-41n+24) binomial(3n-5,n-2)/n/(2n-1)	(5n-4)binomial(3n-3,n-1)/n
E6	833	418	41472	5844	16588
E7	4160	2431	1062882	61866	144210
E8	25080	17342	37968750	808005	1520922
F4	105	66	432	228	780
G2	8	5	6	6	21
H3	32	21	50	40	143
H4	280	232	1350	705	2232
I2(h)	h+2	h-1	h	h	3 h + 3

Références :

• math/0202004 Polytopal realizations of generalized associahedra. Frédéric Chapoton, Sergey Fomin, Andrei Zelevinsky.
• hep-th/0111053 Y-systems and generalized associahedra. Sergey Fomin, Andrei Zelevinsky.
• math/0104151 Cluster algebras I: Foundations. Sergey Fomin, Andrei Zelevinsky.
• math/0208229 Cluster algebras II: Finite type classification Sergey Fomin, Andrei Zelevinsky.