Information on Subsets, Combinations and Product Spaces
This page gives a brief explanation of the input and output options
available on the "Generate Subsets or Combinations" page.
More extensive explanation is given on the following pages.
Subsets
A set is a collection of objects, and a subset is a subcollection of those
objects.
The number of subsets of an n element set is 2^{n}.
In the Object Server, the set from which subsets are made is always
the set [n] of the first n positive integers
(i.e., [n] = {1,2,...,n}).
 Required Input:
 For both subset options, n is a required input.
 Optional Input:

For subsets in lex order, k is an optional input which limits
the subsets output to only those subsets containing no more than
k elements.
 Ignored Input:
 For both subset options, the input values
n_{1},...,n_{6} are ignored.
 Bitstring Output:
 Each subset S is listed as a bitstring
b_{n}···b_{2}b_{1} where
b_{i} = 1 if i is in S and b_{i} = 0 if
i is not in S.

List of Elements Output:
 Each subset S (say of size p) is output
as an ordered list {s_{1},s_{2},...,s_{p}}
of its elements.

Bit Change Output:
 If Gray code is selected under "What Type?", then
the index of the bit that changes is output; furthermove, the bit that changes
is shown in green (in the bitstring output).

Towers of Hanoi Output:
 Ignored unless Gray code selected. Further explanation
on the subset info page.
Combinations

Required Input:
 For all combinations options, n and k are required inputs.

Optional Input:
 None.

Ignored Input:

For all combinations options, the values
n_{1},...,n_{6} are ignored.
 Bitstring Output:
 Each subset S is listed as a bitstring
b_{n}···b_{2}b_{1} where
b_{i} = 1 if i is in S and b_{i} = 0 if
i is not in S.

List of Elements Output:
 Each subset S is output as an ordered list
{s_{1},s_{2},...,s_{p}} of its elements.

Transposition Output:
 If either of the two transposition methods is selected under
"What Type?", then the indices of the two bits that are transposed are output;
furthermove, the transposed bits are shown in green (in the
bitstring output).

Towers of Hanoi Output:
 Ignored.
Product Spaces

Required Input:
 At least one of the values
n_{1},...,n_{6}.

Optional Input:
 None.

Ignored Input:

The values n and k.
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