Dynkin Type Assignment Figure Shows The Scope Of The Exception Sequence

At the 1992 Canadian Mathematical society Annual Seminar, A.N.Rudakov lectured on exceptional sequences of vector bundles for P2. In 1993,W.Crawley-Boevey introduced the concept of exceptional sequences to the representations of quivers(see[CB3]).He proved that the action of the braid group with(n-1) generators on the set of complete exceptional sequences in categories of representations of quivers with n simple representations. In 1994, C.M.Ringel generalized the concept of exceptional sequences and Crawley-Boevey's result to general hereditary artinina algebras, and gave the relationship between complete exceptional sequences and tilting modules. The introduction of exceptional sequences into the representation theory also gave rise to people's notice on the number of complete exceptional sequences.At present , the number of complete exceptional sequences of type A . D(n> 3) F8 have been known (see [Su] . [LS]).In this paper, we are going to deal with all Dynkin diagrams rather than with those having single edges only.In §lwe recall some basic definitions and facts.Jn §2we give the definitions of Hammock over the valued graphs;we point, out a new HammockH(P(a))(see theory 2.1.2); LetH be a valued Hammock ,and p is a projective vertex of H that is different from the source. we prove thatH = E HIHomk(H)(p. z) O}andH/H~ =HIhH(x) - h(H)(x) O}are valued Hammocks,their Hmmock function are h(H~)(-) = dimHomk(H)(p, -)andh(H/H~) = hH - h(H~) (see theory 2.2.1). In §3we give the formulea of the number of complete exceptional sequences of type of B~. C,2. F4. G2 (see theory 3.3.1 and theory 3.3.4).In §4we prove that the action of the braid group is equivalent a reflection on the intersection matrix (or JM).