An algorithm for uniform generation of unlabeled trees (Pólya trees), with an extension of Cayley's formula
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910716980625408 |
|---|---|
| author | Bartholdi, Laurent Diaconis, Persi |
| author_facet | Bartholdi, Laurent Diaconis, Persi |
| contents | Pólya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate Pólya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with `reality'.
Along the way, we give a product formula for the number of rooted labeled trees preserved by a given automorphism; this refines Cayley's formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17613 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An algorithm for uniform generation of unlabeled trees (Pólya trees), with an extension of Cayley's formula Bartholdi, Laurent Diaconis, Persi Combinatorics Group Theory Probability Pólya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate Pólya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with `reality'. Along the way, we give a product formula for the number of rooted labeled trees preserved by a given automorphism; this refines Cayley's formula. |
| title | An algorithm for uniform generation of unlabeled trees (Pólya trees), with an extension of Cayley's formula |
| topic | Combinatorics Group Theory Probability |
| url | https://arxiv.org/abs/2411.17613 |