Function Repository Resource:

# OrderedTupleIndex

Give the index of an ordered tuple

Contributed by: Ed Pegg Jr
 ResourceFunction["OrderedTupleIndex"][tuple] gives the index of the ordered tuple.

## Details and Options

Ordered tuples are considered to be lists {a1,a2,,ak} such that the ai are non-negative and non-decreasing.
For any ordered tuple, a unique index n can be defined via .
For example, subset {1, 2, 2} has index .

## Examples

### Basic Examples (2)

The following ordered 3-tuple sequence can be extended to infinity:

 In[1]:=
 Out[1]=

The function returns indices of one to ten for these ordered tuples:

 In[2]:=
 Out[2]=

Any nondecreasing list of nonnegative integers can be considered as an ordered tuple with a unique index:

 In[3]:=
 Out[3]=

The result above is an ordered tuple with a unique index:

 In[4]:=
 Out[4]=

### Scope (3)

Here are some ordered 2-tuples with their indices to show their structure:

 In[5]:=
 Out[5]=

The ordered 2-tuple {4,4} has an index of :

 In[6]:=
 Out[6]=

OrderedTupleIndex returns the same thing:

 In[7]:=
 Out[7]=

The structure of ordered 3-tuples in 3D:

 In[8]:=
 Out[8]=

### Properties and Relations (3)

Use Tuples to produce ordered 3-tuples:

 In[9]:=
 Out[9]=

The same sequence of ordered 3-tuples can be obtained from ordered Subsets:

 In[10]:=
 Out[10]=

Indices of this sequence:

 In[11]:=
 Out[11]=

## Version History

• 1.0.0 – 06 December 2019