Read e-book online Combinatoire énumérative: Proceedings of the “Colloque de PDF

By A. K. Agarwal (auth.), Gilbert Labelle, Pierre Leroux (eds.)

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Extra resources for Combinatoire énumérative: Proceedings of the “Colloque de combinatoire énumérative”, held at Université du Québec à Montréal, May 28 – June 1, 1985

Sample text

N be linear combinatorial species. +an~n, the set K [ ~ I , ~ 2 ..... ~n] w i t h coefficients operators over the same category of of formal linear in a ring K with unity. We w i l l operators for which it can be shown that all Lie brackets [ ~ i , ~ j ] = ~ i ~ j - compositions work w i t h ~j~i , for l~i,j~,n, are linear combinations of a31,~ 2, ... ,~n • Thus we clearly have a Lie algebra structure on K[01~1,~2, _. ,~n]- EX,~PLE: Let ~1 = 8,8X , ~2 = X$/SX and ~3 [~2,~3]=~3 = x2 8/8X .

Us(l+J) l-us(l+J) + des cartes de ~ e s t 0 4 j ~ r, pour reconstituer la variable l'on concat~ne les uplets Bj le bord de H, le produit des s6ries g@n&- (d@termin6es ci-dessus) s, t o u s l e s (cf (a)) z (f. z card(~ ,r)safBa~)(l_us(l+j))r r>~l a>~O,B>~O,v>~O ,S,y Le terme ~i est dfi au fair que lorsque ratrices associ@es done d@compte, par l'exposant de sommets du bord de H, y compris le sommet point@ 19 (ce qui est exclu darts la d~finition de J). On en d~duit J = ~ u(l+J) 1 [a + f K(l-us'l+J''~) , s,f,a)] L CQFD 2.

We assume the reader to be familiar with elementary notions of formal languages the~y [Har 78]. I I . am,a1,... ,~9""(~" and the associated right parentheses : )I" )2"'")m ; it is convenient to denote these parentheses as the letters of an alphabet A ={a I .... am, aq .... a"m}" Let L be the language of the two-sided well-balanced parentheses over A, generated by the simple grammar : S'4w ai S~ S + ~'i S ai S + E , i=I to m [Har 78]. 1 (i=I to m) [Ber 79] . ) f o r the axiom). Because of : on the one hand, the symmetry between l 1 the r u l a b e g i n n i n g by Si ~ , and the corresponding other hand, the symmetry of the p a r t s of the l e t t e r s r u l a b e g i n n i n g by ~'i--~ ; on the a l , .

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