# HYBRID d-ARY TREES AND THEIR GENERALIZATION

• Published : 2014.01.31

#### Abstract

We enumerate black and white colored d-ary trees with no leftmost ${\square}$-edges, which is a generalization of hybrid binary trees. Then the multi-colored hybrid d-ary trees with the same condition is studied.

#### References

1. N. Gu, N. Li, and T. Mansour, 2-Binary trees: Bijections and related issues, Discrete Math. 308 (2008), no. 7, 1209-1221. https://doi.org/10.1016/j.disc.2007.04.007
2. N. Gu and H. Prodinger, Bijections for 2-plane trees and ternary trees, European J. Combin. 30 (2009), no. 4, 969-985. https://doi.org/10.1016/j.ejc.2008.06.006
3. J. Pallo, On the listing and random generation of hybrid binary trees, Int. J. Computer Math. 50 (1994), 135-145. https://doi.org/10.1080/00207169408804251
4. A. Panholzer and H. Prodinger, Bijections between certain families of labelled and unlabelled d-ary trees, Appl. Anal. Discrete Math. 3 (2009), no. 1, 123-136. https://doi.org/10.2298/AADM0901123P
5. R. P. Stanley, Enumerative Combinatorics. Vol. 2, Cambridge University Press, Cambridge, 1999.
6. S. Yan and X. Liu, 2-noncrossing trees and 5-ary trees, Discrete Math. 309 (2009), no.20, 6135-6138. https://doi.org/10.1016/j.disc.2009.03.044