By A. K. Agarwal (auth.), Gilbert Labelle, Pierre Leroux (eds.)
Read Online or Download Combinatoire énumérative: Proceedings of the “Colloque de combinatoire énumérative”, held at Université du Québec à Montréal, May 28 – June 1, 1985 PDF
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Additional resources for Combinatoire énumérative: Proceedings of the “Colloque de combinatoire énumérative”, held at Université du Québec à Montréal, May 28 – June 1, 1985
Lie bracket Throughout this text, a typical structure t of a typical species T w i i i be represented by the following picture: $7 i"-~ I Figure 3. I Here, the white circles represent labelled points of type "X"; and black squares, labelled points of type "Y". The thick lines are there to help distinguish between points of the two kinds. The labels are not shown for simplicity's sake. Thus, the effect of a combinatorial operator Z~, can be illustrated by showing how typical structures of species ~T, may be constructed out of T-structures (structures of species T).
Note that t$/St , as a combinatorial operator, corresponds to pointing a dotted circular point. Thus we can see that the effect of ~1 , on Ft-structures, is to replace a circular point, without dotted pattern, by a point of type Y. Moreover, the action of ~ on typical Ft-structures , is that of adding a new point in one of the four following ways: The 43 first and second one (corresponding to tX and o(X), add an isolated point respectively with weight t (dotted circular point) or o(. The last two possibilities (X2 6/5X and tX$/St), both attach a new point to a previously selected one.
4) emm ma lwll - : L e t W E P ~ A " : wgL, w = wl w2, w,$P, w2 #E; then L(n+1)/21. e- f = (fTIT = k T hT, kfe; i=2 ~ ( n + l /zJ ) 5n=m ;62n-1= q n = r n n - f i=2 1 EL, "oaf %z)= : (7) mz2 = g ( Z ) = mZ2 mz2 + (I+L) so ( ;drz>/l 2 8, (3) rnn-') si , whence t ( n + ~ /2 ) J- i I m a f u n c t i o n a l e q u a t i o n f o r B c a n be o b t a i n e d : - (m2z4/1 mZ2) +S2s2" (zZn-' Zn = 5 2 z 2 11 - mz) changing Z i n t o 5(z2)/1 i i=2 n-i (mn n22 = (m becomes : Z ( Z 2 ) / 1 - - ( z ( ~ ( z )+ Z.
Combinatoire énumérative: Proceedings of the “Colloque de combinatoire énumérative”, held at Université du Québec à Montréal, May 28 – June 1, 1985 by A. K. Agarwal (auth.), Gilbert Labelle, Pierre Leroux (eds.)