Abstract
One of the most beautiful formulas in enumerative combinatorics concerns the number of labeled trees. Consider the set N = {1, 2, . . . , n}. How many different trees can we form on this vertex set? Let us denote this number by T n . Enumeration “by hand” yields T 1 = 1, T 2 = 1, T 3 = 3, T 4 = 16, with the trees shown in the following table:
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Aigner, M., Ziegler, G.M. (2014). Cayley’s formula for the number of trees. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44205-0_32
Download citation
DOI: https://doi.org/10.1007/978-3-662-44205-0_32
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-44204-3
Online ISBN: 978-3-662-44205-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)