Counting Colored Trees
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910025550659584 |
|---|---|
| author | Dimitrov, Stoyan Fox, Nathan Hadaway, Kimberly Tharp, Ashley Wagner, Stephan |
| author_facet | Dimitrov, Stoyan Fox, Nathan Hadaway, Kimberly Tharp, Ashley Wagner, Stephan |
| contents | We consider the enumeration of plane trees (rooted ordered trees) whose vertices are colored according to a specific coloring rule that prescribes which possible pairs of colors can occur as the colors of a parent vertex and its child. This general construction covers many different examples that have been studied in the literature. Some general necessary and sufficient conditions for two different coloring rules to result in the same counting sequence are established. We also provide exhaustive lists of counting sequences arising from coloring rules with two or three colors, and we find formulas and closed form expressions for many of these sequences. The famous Fibonacci, Catalan, Narayana, and Schröder sequences appear in several cases. Some of these coloring rules are extended to families of coloring rules with arbitrarily many colors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16055 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting Colored Trees Dimitrov, Stoyan Fox, Nathan Hadaway, Kimberly Tharp, Ashley Wagner, Stephan Combinatorics 05A15 (Primary) 05A19, 05C05, 05C30 (Secondary) We consider the enumeration of plane trees (rooted ordered trees) whose vertices are colored according to a specific coloring rule that prescribes which possible pairs of colors can occur as the colors of a parent vertex and its child. This general construction covers many different examples that have been studied in the literature. Some general necessary and sufficient conditions for two different coloring rules to result in the same counting sequence are established. We also provide exhaustive lists of counting sequences arising from coloring rules with two or three colors, and we find formulas and closed form expressions for many of these sequences. The famous Fibonacci, Catalan, Narayana, and Schröder sequences appear in several cases. Some of these coloring rules are extended to families of coloring rules with arbitrarily many colors. |
| title | Counting Colored Trees |
| topic | Combinatorics 05A15 (Primary) 05A19, 05C05, 05C30 (Secondary) |
| url | https://arxiv.org/abs/2602.16055 |