Graphs in Perturbation Theory by Michael Borinsky

Author:Michael Borinsky
Language: eng
Format: epub
ISBN: 9783030035419
Publisher: Springer International Publishing

4.6.2 Monolithic Chord Diagrams

A chord diagram is called monolithic if it consists only of a connected component and of isolated chords which do not ‘contain’ each other [11]. That means with (a, b) and (c, d) the labels of two chords, it is not allowed that nor . Let be the generating function of monolithic chord diagrams. Following [11], M(x) fulfills

(4.6.7)

Clearly, Theorem 4.4.2 implies that , because and . Using the -derivation on both sides of this equation together with the result for in Eq. (4.6.5) gives

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