On embedded trees and lattice paths

Details On embedded trees and lattice paths On embedded trees and lattice paths

2009-06-02

arxiv.org/abs/0906.0450v4

Mathematics

Combinatorics

19 pages, 2 Figures; typos corrected; Section 8 added

Scientific paper

Bouttier, Di Francesco and Guitter introduced a method for solving certain classes of algebraic recurrence relations arising the context of embedded trees and map enumeration. The aim of this note is to apply this method to three problems. First, we discuss a general family of embedded binary trees, trying to unify and summarize several enumeration results for binary tree families, and also to add new results. Second, we discuss the family of embedded $d$-ary trees, embedded in the plane in a natural way. Third, we show that several enumeration problems concerning simple families of lattice paths can be solved without using the kernel method by regarding simple families of lattice paths as degenerated families of embedded trees.

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