Basic Examples (3)
Basic Examples
(3)
Here is the simplest nontrivial example with two pairs of brackets:
In[1]:=
Out[1]=
{[[]],[][]}
———
Here are the ways to nest three pairs of brackets:
In[1]:=
Out[1]=
{[[[]]],[[][]],[[]][],[][[]],[][][]}
There are five ways to do that:
In[2]:=
Length@%
Out[2]=
5
———
Dyck words are counted by the Catalan numbers:
In[1]:=
Length@[#]&/@Range[10]
Out[1]=
{1,2,5,14,42,132,429,1430,4862,16796}
In[2]:=
CatalanNumber@Range@10
Out[2]=
{1,2,5,14,42,132,429,1430,4862,16796}
Scope (2)
Scope
(2)