Enumeration of m-ary cacti
| dc.creator | Bona, Miklos | |
| dc.creator | Bousquet, Michel | |
| dc.creator | Labelle, Gilbert | |
| dc.creator | Leroux, Pierre | |
| dc.date | 1998-04-24 | |
| dc.date | 1999-01-28 | |
| dc.date.accessioned | 2026-07-07T05:24:36Z | |
| dc.date.available | 2026-07-07T05:24:36Z | |
| dc.description | The purpose of this paper is to enumerate various classes of cyclically colored m-gonal plane cacti, called m-ary cacti. This combinatorial problem is motivated by the topological classification of complex polynomials having at most m critical values, studied by Zvonkin and others. We obtain explicit formulae for both labelled and unlabelled m-ary cacti, according to i) the number of polygons, ii) the vertex-color distribution, iii) the vertex-degree distribution of each color. We also enumerate m-ary cacti according to the order of their automorphism group. Using a generalization of Otter's formula, we express the species of m-ary cacti in terms of rooted and of pointed cacti. A variant of the m-dimensional Lagrange inversion is then used to enumerate these structures. The method of Liskovets for the enumeration of unrooted planar maps can also be adapted to m-ary cacti. | |
| dc.description | LaTeX2e, 28 pages, 9 figures (eps), 3 tables | |
| dc.identifier | https://arxiv.org/abs/math/9804119 | |
| dc.identifier | http://arxiv.org/abs/math/9804119 | |
| dc.identifier | Advances in Applied Mathematics, 24 (2000), 22-56 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76863 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15 (Primary), 05C30 (Secondary) | |
| dc.title | Enumeration of m-ary cacti | |
| dc.type | text |