A note on enumeration of one-vertex maps

作者：Orbanic Alen^*; Petkovsek Marko; Pisanski Tomaz; Potocnik Primoz

来源：Ars Mathematica Contemporanea, 2010, 3(1): 1-12.

• Oriented maps and pre-maps
• orientable maps and pre-maps
• non-orientable maps and pre-maps
• pre-graphs
• matchings in complete graphs
• Cauchy-Frobenius-Burnside lemma

Explicit formulae for the numbers of distinct maps and pre-maps having a single vertex of valence d are given. The question of what precisely is meant by a map can be answered in several different ways. We enumerate 16 different types of objects where each type is obtained by selecting whether the object is a pre-map or a map, is oriented or general, whether the underlying graph or pre-graph is signed or unsigned, is directed or undirected.

• 出版日期2010