Academic Journal
On Stahl's conjectures about the region distributions of bouquets
| Title: | On Stahl's conjectures about the region distributions of bouquets |
|---|---|
| Authors: | Yichao Chen, Zhicheng Gao |
| Source: | Journal of Graph Theory. 109:201-209 |
| Publisher Information: | Wiley, 2023. |
| Publication Year: | 2023 |
| Subject Terms: | embedding, region distribution, median, Exact enumeration problems, generating functions, mode, 0102 computer and information sciences, 0101 mathematics, Enumeration in graph theory, Asymptotic enumeration, 01 natural sciences, Planar graphs, geometric and topological aspects of graph theory |
| Description: | Let denote the graph with one vertex and loops, and be the number of embeddings of with regions in an orientable surface. Stahl conjectured that both the mode and the median of the sequence are within one unit of the harmonic number . In this paper we will confirm the conjecture about the median and disprove the conjecture about the mode. We will show that the mode of the sequence belongs to the set , and each of these three values can be attained by infinitely many . |
| Document Type: | Article |
| File Description: | application/xml |
| Language: | English |
| ISSN: | 1097-0118 0364-9024 |
| DOI: | 10.1002/jgt.23029 |
| Rights: | Wiley Online Library User Agreement |
| Accession Number: | edsair.doi.dedup.....9e8d8d85865101e3bf08e4f080dd49fa |
| Database: | OpenAIRE |
| ISSN: | 10970118 03649024 |
|---|---|
| DOI: | 10.1002/jgt.23029 |