Function Repository Resource:

SubsetFromIndex

Source Notebook

Get the subset with the given index and length

Contributed by: Ed Pegg Jr

ResourceFunction["SubsetFromIndex"][index,len]

returns a subset of length len with given index.

Details and Options

Subsets are considered to be lists {a₁,a₂,…,a_k} such that the a_i are non-negative integers and strictly increasing.

Subsets are sorted by their reverse; {1,2,3} comes before {0,1,4}.

For any subset, a unique index n can be defined via

For example: subset {2,4,6} has index

Examples

Basic Examples (3)

Give the first ten 3-subsets:

In[1]:=

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The following code gives the same 3-subset sequence:

In[2]:=

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The function can return subsets of a large index:

In[3]:=

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The function can return the subset of a given index for various lengths:

In[4]:=

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Scope (3)

Some binomial representations of the number 320:

In[5]:=

Column[Row[
Riffle[Table[
TraditionalForm[
Binomial[(ToString /@ #)[[n]], ToString[n]]], {n, 1, Length[#]}], "+"]] & /@ Table[ResourceFunction["SubsetFromIndex"][321, n], {n, 2, 7}], Alignment -> Center]

Out[5]=

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

In[6]:=

doubles = Table[{ResourceFunction["SubsetFromIndex"][index, 2], index}, {index, 1, 15}];
Graphics[{Text[Style[Column[{StringJoin[ToString /@ #[[1]]], #[[2]]},
Alignment -> Center], 20], #[[1]]] & /@ doubles, Blue, Line[First /@ doubles]}]

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The structure of 3-subsets in 3D:

In[7]:=

triples = Table[{ResourceFunction["SubsetFromIndex"][index, 3], index}, {index, 1, 20}];
Graphics3D[{Text[Style[Column[{StringJoin[ToString /@ #[[1]]], #[[2]]},
Alignment -> Center], 20], #[[1]]] & /@ triples, Blue, Line[First /@ triples]}]

Out[7]=

Neat Examples (1)

Find the trillionth numbers with binary weights eight to twelve:

In[8]:=

$Column[Table[ Total[2^ResourceFunction["SubsetFromIndex"][10^12, weight]], {weight, 8, 12}]]$

Out[8]=

Version History

2.0.0 – 24 December 2019
1.0.0 – 05 December 2019

Related Resources

License Information

This work is licensed under a Creative Commons Attribution 4.0 International License