A bijection

1
Combinatorics and permutations avoiding 3-letter
pattern
The decomposition representation
Dyck paths
The diagram
Continued fructions And Ordered trees
Tunnels and Dyck paths
Dyck paths
if and only if For some tree T
A bijection
A generating function that enumerate the of
For
A generating function That enumerate the Number
of That contain ones
There is a bijection between and Dyck
baths
A bijection between And Dyck paths
There exist that For
The generating Function As a continued fraction
The generating Function of the set
With the same number of Fixed points and
excedances
The number of Permutations in With r
occurrences Of the pattern 12k
An asymptotic Estimate for With r occurrences Of
the pattern 12k
A generating function As a continued
fructions That enumerates Permutations By
number of patterns 12k
Enumerate the set Of that Contain 12k
ones
A combinatorics proof of For any integers
n,k and kgt2 For any kgt2
Enumerate the set With r occurrences
of (k-1)1k
The generating function As a continued
fructions
We have the following result
An analitic proof of For d1,2,,k-1. Yet,
there is no combinatorics proof.