中央研究院 数學研咒所 Theorem: Let S=((, 1 )U(( -i+1)i=1,2 W(O)=(-+1)=an Let L,= l (s) be the set of s-nonnegativ e paths with endpoint(n,0 andL=L(S)=∪, Define a generating function=∑∑w(P) ≥0P∈L Then 件()=1+∑∑a2f() 1=1 J 1+f(=)°·F(=,f(=) 第11页第11页 1 ( ) ( , ( )). Then 1 [ ( )] and ( ) .Define a generating function ( ) . Let ( ) be the set of S- nonnegativ e paths with endpoint (n,0) (01) 1 ( 1) . Theorem :Let {(0,1)} {( , 1) 1,2, , 1,2, , )} 1 1 0 0 zf z F z f z f(z) a z f z L L S L f(z) w P z L L S w , ,w j,-i a S j i i r j m j i r i m j i j n P L n n n n n i j n = + • = + = = = = = + = =  − + = =    = =      