Enumeration of non-positive planar trivalent graphs

Details Enumeration of non-positive planar trivalent graphs Enumeration of non-positive planar trivalent graphs

2005-07-06

arxiv.org/abs/math/0507112v1

J Algebr Comb (2007) 25:357-373

Mathematics

Combinatorics

Scientific paper

10.1007/s10801-006-0041-4

In this paper we construct inverse bijections between two sequences of finite sets. One sequence is defined by planar diagrams and the other by lattice walks. G. Kuperberg has shown that the number of elements in these two sets are equal. This problem and the methods we use are motivated by the representation theory of the exceptional simple Lie algebra $G_2$. However in this account we have emphasised the combinatorics.

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